Question 13 Marks
Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.
Answer
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3 Marks Question
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44 questions · self-marked practice — reveal the answer and mark yourself.
Question 23 Marks
Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from the centre. Construct tangents to the circle from point Q.
Answer
View full question & answer→Steps of construction:
i. Draw a circle with center P and radius 3.4 cm.
ii. Take a point Q outside the circle such that PQ = 5.5 cm
iii. Draw the perpendicular bisector of PQ, which bisects PQ at O.
iv. Taking O as center and OP = OQ as radius, draw another circle, which intersects the previous circle at A and B.
v. Join AQ and BQ, which are required tangents.
i. Draw a circle with center P and radius 3.4 cm.
ii. Take a point Q outside the circle such that PQ = 5.5 cm
iii. Draw the perpendicular bisector of PQ, which bisects PQ at O.
iv. Taking O as center and OP = OQ as radius, draw another circle, which intersects the previous circle at A and B.
v. Join AQ and BQ, which are required tangents.
Question 33 Marks
Draw a circle of radius 3.3 cm Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q. Write your observation about the tangents.
Answer
View full question & answer→Here chord = 6.6 = 2 × 3.3 cm = 2 × radius, hence PQ is diameter of the circle.
Steps of construction:
i. Draw a circle with center O, and radius 3.3 cm
ii. Draw a diameter PQ passing through center.
iii. Draw AB ⊥ OQ and CD ⊥ OP , such that AB and CD pass through Q and P respectively.
iv. AB and CD are required tangents.
Observation: AB || CD, i.e. tangents at opposite ends of diameter are parallel.
Steps of construction:
i. Draw a circle with center O, and radius 3.3 cm
ii. Draw a diameter PQ passing through center.
iii. Draw AB ⊥ OQ and CD ⊥ OP , such that AB and CD pass through Q and P respectively.
iv. AB and CD are required tangents.
Observation: AB || CD, i.e. tangents at opposite ends of diameter are parallel.
Question 43 Marks
Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.
Answer
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Question 53 Marks
Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.
Answer
View full question & answer→Steps of construction:
i. Draw a circle with center P and radius 2.7 cm
ii. Take a point M on the circle, Join PM.
iii. Draw AB ⊥ PM such that AB passes through M, AB is required tangent.
i. Draw a circle with center P and radius 2.7 cm
ii. Take a point M on the circle, Join PM.
iii. Draw AB ⊥ PM such that AB passes through M, AB is required tangent.
Question 63 Marks
Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.
Answer
View full question & answer→Steps of construction:
i. Draw a circle with center P and radius 3.2 cm
ii. Take a point M on the circle, Join PM.
iii. Draw AB ⊥ PM such that AB passes through M, AB is required tangent.
i. Draw a circle with center P and radius 3.2 cm
ii. Take a point M on the circle, Join PM.
iii. Draw AB ⊥ PM such that AB passes through M, AB is required tangent.
Question 73 Marks
∆ AMT ~ ∆ AHE. In ∆ AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm.$\frac{AM}{AH} = \frac{7}{5}.$Construct ∆ AHE.
Answer
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Question 83 Marks
∆ RST ~ ∆ XYZ. In ∆ RST, RS = 4.5 cm, ∠RST = 40°, ST = 5.7 cm. Construct ∆ RST and ∆XYZ, such that $\frac{ RS }{ XY }=\frac{3}{5}$
Answer
View full question & answer→First we draw a triangle RST, with RS = 4.5 cm, ∠RST = 40° cm and ST = 5.7 cm
Now, as ΔRST is similar to ΔXYZ,
∴ corresponding sides will have same ratio
Now, as $\frac{ RS }{ XY }=\frac{3}{5}$
$\Rightarrow \frac{ RS }{ XY }=\frac{ ST }{ YZ }=\frac{ TR }{ ZX }=\frac{3}{5}$
$\Rightarrow \frac{4.5}{ XY }=\frac{3}{5}$
$\Rightarrow XY =7.5 cm$
$\Rightarrow \frac{5.7}{ YZ }=\frac{3}{5}$
⇒ YZ = 9.5 cm
Also, Corresponding angles of similar triangles are equal
⇒ ∠RST = ∠XYZ = 40°
Now, draw a triangle XYZ, with XY = 7.5 cm, ∠XYZ = 40° cm and YZ = 9.5 cm.
Now, as ΔRST is similar to ΔXYZ,
∴ corresponding sides will have same ratio
Now, as $\frac{ RS }{ XY }=\frac{3}{5}$
$\Rightarrow \frac{ RS }{ XY }=\frac{ ST }{ YZ }=\frac{ TR }{ ZX }=\frac{3}{5}$
$\Rightarrow \frac{4.5}{ XY }=\frac{3}{5}$
$\Rightarrow XY =7.5 cm$
$\Rightarrow \frac{5.7}{ YZ }=\frac{3}{5}$
⇒ YZ = 9.5 cm
Also, Corresponding angles of similar triangles are equal
⇒ ∠RST = ∠XYZ = 40°
Now, draw a triangle XYZ, with XY = 7.5 cm, ∠XYZ = 40° cm and YZ = 9.5 cm.
Question 93 Marks
∆ PQR ~ ∆ LTR. In ∆ PQR, PQ = 4.2 cm, QR = 5.4 cm, PR = 4.8 cm. Construct ∆ PQR and ∆ LTR, such that $\frac{PQ}{LT} = \frac{3}{4}.$
Answer
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Question 103 Marks
∆ ABC ~ ∆ LMN. In ∆ ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ∆ ABC and ∆ LMN such that $\frac{ BC }{ MN }=\frac{5}{4}$.
Answer
View full question & answer→First we draw a triangle ABC, with AB = 5.5 cm, BC = 6 cm and CA = 4.5 cm
Now, as ΔABC is similar to ΔLMN
∴ corresponding sides will have same ratio
Now, as $\frac{B C}{M N}=\frac{5}{4}$
$\Rightarrow \frac{ AB }{ LM }=\frac{ BC }{ MN }=\frac{ AC }{ LN }=\frac{5}{4}$
$\Rightarrow \frac{5.5}{ LM }=\frac{5}{4}$
$\Rightarrow LM =4.4 cm$
$\Rightarrow \frac{6}{ MN }=\frac{5}{4}$
$\Rightarrow MN =4.8 cm$
$\Rightarrow \frac{4.5}{ LN }=\frac{5}{4}$
⇒ LN = 3.6 cm
Now, make a ΔLMN, with LM = 4.4 cm, MN = 4.8 cm and LN = 3.6 cm
Now, as ΔABC is similar to ΔLMN
∴ corresponding sides will have same ratio
Now, as $\frac{B C}{M N}=\frac{5}{4}$
$\Rightarrow \frac{ AB }{ LM }=\frac{ BC }{ MN }=\frac{ AC }{ LN }=\frac{5}{4}$
$\Rightarrow \frac{5.5}{ LM }=\frac{5}{4}$
$\Rightarrow LM =4.4 cm$
$\Rightarrow \frac{6}{ MN }=\frac{5}{4}$
$\Rightarrow MN =4.8 cm$
$\Rightarrow \frac{4.5}{ LN }=\frac{5}{4}$
⇒ LN = 3.6 cm
Now, make a ΔLMN, with LM = 4.4 cm, MN = 4.8 cm and LN = 3.6 cm
Question 113 Marks
construct tangents to a circle from a point outside the circle.
Question 123 Marks
Construction of a tangent to a circle at a point on the circle Without using the centre of the circle.
Question 133 Marks
Construction of a tangent to a circle at a point on the circle Using the centre of the circle.
Question 143 Marks
Construct D A'BC' similar to D ABC such that AB:A'B = 5:7
Question 153 Marks
Construct any $\triangle \mathrm{ABC}$. Construct $\triangle \mathrm{A}^{\prime} \mathrm{BC}^{\prime}$ such that $\mathrm{AB}: \mathrm{A}^{\prime} \mathrm{B}=5: 3$ and $\Delta \mathrm{ABC} \sim \Delta \mathrm{A}^{\prime} \mathrm{BC}^{\prime}$
View full question & answer→Question 163 Marks
$\triangle \mathrm{ABC} \sim \triangle \mathrm{PQR}$, in $\triangle \mathrm{ABC}, \mathrm{AB}=5.4 \mathrm{~cm}, \mathrm{BC}=4.2 \mathrm{~cm}, \mathrm{AC}=6.0 \mathrm{~cm}$.
$\mathrm{AB}: \mathrm{PQ}=3: 2$. Construct $\triangle \mathrm{ABC}$ and $\triangle \mathrm{PQR}$.
View full question & answer→$\mathrm{AB}: \mathrm{PQ}=3: 2$. Construct $\triangle \mathrm{ABC}$ and $\triangle \mathrm{PQR}$.
Question 173 Marks
Draw a circle with 'O' as centre and radius 3.8 cm. Take two points P and Q such that $\angle$POQ = 120° Draw tangents at P and Q without using centre.
Answer
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Question 183 Marks
Draw a circle with centre M and diameter 6 cm. Draw a tangent to the circle from a point N at distance of 9 cm from the centre.
Answer
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Question 193 Marks
Construct a circle with centre 'O' and radius 4.3 cm. Draw a chord AB of length 5.6 cm. Construct the tangents to the circle at point A and B without using centre.
Answer
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Question 203 Marks
Draw a circle with centre 'P' and radius 2.6 cm. Draw a chord AB of length 3.8 cm. Draw tangent to the circle through points A and B.
Answer
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Question 213 Marks
Draw a tangent to a circle of radius 3 cm and centre 'O' at any point 'K' on the circle.
Answer
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Question 223 Marks
$\triangle X Y Z \sim \Delta ABC , \angle X=40^{\circ}, \angle Y=80^{\circ}, X Y=6 cm$. Draw $\triangle ABC$, if $AB : XY =3: 2$
Answer
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Question 233 Marks
Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.
Question 243 Marks
Draw a circle with centre P and radius 3.4 cm. Take point Q at a distance 5.5 cm from the centre. Construct tangents to the circle from point Q.
Question 253 Marks
Draw a circle of radius 3.3 cm Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q. Write your observation about the tangents.
Question 263 Marks
Draw a circle of radius 3.6 cm. Draw a tangent to the circle at any point on it without using the centre.
Question 273 Marks
Draw a circle of radius 2.7 cm. Draw a tangent to the circle at any point on it.
Question 283 Marks
Construct a tangent to a circle with centre P and radius 3.2 cm at any point M on it.
Question 293 Marks
$\Delta AMT \sim \Delta AHE . \ln \Delta AMT , AM =6.3 cm , \angle TAM =50^{\circ}, AT =5.6 cm . \frac{ AM }{ AH }=\frac{7}{5}$. Construct $\triangle AHE$.
View full question & answer→Question 303 Marks
$\Delta R S T \sim \Delta X Y Z$. In $\Delta R S T, R S=4.5 cm , \angle R S T=40^{\circ}, S T=5.7 cm$. Construct $\Delta R S T$ and $\Delta X Y Z$, such that $\frac{ RS }{X Y}=\frac{3}{5}$.
View full question & answer→Question 313 Marks
$\Delta P Q R \sim \Delta L T R . \ln \Delta P Q R, P Q=4.2 cm , Q R=5.4 cm , P R=4.8 cm$. Construct $\Delta P Q R$ and $\Delta L T R$, such that $\frac{P Q}{L T}=\frac{3}{4}$.
View full question & answer→Question 323 Marks
$\triangle A B C \sim \Delta L M N$. In $\triangle A B C, A B=5.5 cm , B C=6 cm , C A=4.5 cm$. Construct $\triangle A B C$ and $\triangle L M N$ such that $\frac{B C}{M N}=\frac{5}{4}$.
View full question & answer→Question 333 Marks
construct tangents to a circle from a point outside the circle.
Question 343 Marks
Construction of a tangent to a circle at a point on the circle Without using the centre of the circle.
Question 353 Marks
Construction of a tangent to a circle at a point on the circle Using the centre of the circle.
Question 363 Marks
Construct D A'BC' similar to D ABC such that AB:A'B = 5:7
Question 373 Marks
Construct any $\triangle \mathrm{ABC}$. Construct $\triangle \mathrm{A}^{\prime} \mathrm{BC}^{\prime}$ such that $\mathrm{AB}: \mathrm{A}^{\prime} \mathrm{B}=5: 3$ and $\Delta \mathrm{ABC} \sim \Delta \mathrm{A}^{\prime} \mathrm{BC}^{\prime}$
View full question & answer→Question 383 Marks
$\triangle \mathrm{ABC} \sim \triangle \mathrm{PQR}$, in $\triangle \mathrm{ABC}, \mathrm{AB}=5.4 \mathrm{~cm}, \mathrm{BC}=4.2 \mathrm{~cm}, \mathrm{AC}=6.0 \mathrm{~cm}$.
$\mathrm{AB}: \mathrm{PQ}=3: 2$. Construct $\triangle \mathrm{ABC}$ and $\triangle \mathrm{PQR}$.
View full question & answer→$\mathrm{AB}: \mathrm{PQ}=3: 2$. Construct $\triangle \mathrm{ABC}$ and $\triangle \mathrm{PQR}$.
Question 393 Marks
$\triangle X Y Z \sim \Delta ABC , \angle X=40^{\circ}, \angle Y=80^{\circ}, X Y=6 cm$. Draw $\triangle ABC$, if $AB : XY =3: 2$
View full question & answer→Question 403 Marks
Draw a tangent to a circle of radius 3 cm and centre 'O' at any point 'K' on the circle.
Question 413 Marks
Draw a circle with 'O' as centre and radius 3.8 cm. Take two points P and Q such that $\angle$POQ = 120° Draw tangents at P and Q without using centre.
View full question & answer→Question 423 Marks
Draw a circle with centre 'P' and radius 2.6 cm. Draw a chord AB of length 3.8 cm. Draw tangent to the circle through points A and B.
Question 433 Marks
Draw a circle with centre M and diameter 6 cm. Draw a tangent to the circle from a point N at distance of 9 cm from the centre.
Question 443 Marks
Construct a circle with centre 'O' and radius 4.3 cm. Draw a chord AB of length 5.6 cm. Construct the tangents to the circle at point A and B without using centre.