1 Marks Question - MATHS STD 10 Questions - Vidyadip

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28 questions · timed · auto-graded

Question 11 Mark

Fill in the blanks:
The common point of a tangent and the circle is called ..........

Answer

The common point of a tangent and the circle is called point of contact. In fig AB is tangent line P is point of contact between circles and tangent line.

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Question 21 Mark

Fill in the blanks:The angle between tangent at a point on a circle and the radius through the point is ........

Answer

The angle between tangent at a point on a circle and the radius through the point is 90°.

In fig, AB is tengent line P is point of contact O. P is radius. So, angle between OP and AB is 90°.

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Question 31 Mark

Fill in the blanks:A tangent to a circle intersects in it ............ point(s).

Answer

A tangent to a circle intersects in it one point(s).
In fig AB is tengent line.
P is point of contact between circle and tangent line.

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Question 41 Mark

Fill in the blanks:
A circle may have .............. parallel tangents.

Answer

A circle may have two parallel tangents.

In fig. AB is tengent line of circle at point P. CD is tangent line of circle at point Q. $\therefore$ both AB and CD are parallel to each other.

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Question 51 Mark

Fill in the blanks:A line intersecting a circle in two points is called a ..........

Answer

A line intersecting a circle in two points is called a Secant.

In fig AB is secant. AB intersect a circle in 2 point P and Q.

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Question 61 Mark

In Fig. BOA is a diameter of a circle and the tangent at a point P meets BA produced at T.
If $\angle P B O=30^{\circ}$, then find $\angle P T A$. Also, show that AP = AT.

Answer

$30^{\circ}$

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Question 71 Mark

In Fig. PQL and PRM are tangents to the circle with centre O at the points Q and R respectively and S is a point on the circle such that $\angle S Q L=50^{\circ}$ and $\angle S R M=60^{\circ}$. Then find $\angle Q S R$.

Answer

$70^{\circ}$

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Question 81 Mark

In Fig. PQ is a chord of a circle and PT is the tangent at P such that $\angle Q P T = 60^{\circ}$. Then, find $\angle P R Q$.

Answer

$120^{\circ}$

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Question 91 Mark

In Fig. $\triangle P Q R$ circumscribes the circle. If PX = 10 cm, QY = 8 cm and RZ = 6 cm, then find the perimeter of $\triangle P Q R$.

Answer

48 cm

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Question 101 Mark

The length of a chord of a bigger circle concentric with a circle of radius 3 cm is 8 cm. If the chord is a tangent to the smaller circle, then find the radius of the bigger circle.

Answer

5 cm

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Question 111 Mark

If two tangents inclined at angle of $60^{\circ}$ are drawn to a circle of radius 3 cm, then find the length of each tangents.

Answer

$3 \sqrt{3} cm$

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Question 121 Mark

In Fig. AB and CD are tangents to a circle centred at O. Is $\angle B A C=\angle D C A$? Justify your answer.

Answer

Yes, $\angle O A C=\angle O C A$ and $\angle B A O=\angle D C O=90^{\circ}$

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Question 131 Mark

In Fig. PA is a tangent to the circle drawn from the external point P and PBC is the secant to the circle with BC as diameter. If $\angle A O C=130^{\circ}$, then find the measure of $\angle A P B$, where O is the centre of the circle.

Answer

$40^{\circ}$

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Question 141 Mark

AB and AC are tangents drawn from a point A to a circle with centre O. If $\angle B A C=65^{\circ}$, then find the measure of $\angle B O C$.

Answer

$115^{\circ}$

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Question 151 Mark

In Fig. if tangents PA and PB drawn from a point P to a circle with centre O, are inclined to each other at an angle of $70^{\circ}$, then find the measure of $\angle P O A$.

Answer

$55^{\circ}$

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Question 161 Mark

In Fig.XAY is a tangent to the circle centered at O. If $\angle A B O=40^{\circ}$, then find $m \angle B A Y$ and $m \angle A O Y$.

Answer

$\angle B A Y=50^{\circ}, \angle A O B=100^{\circ}$

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Question 171 Mark

In Fig. AB is diameter of a circle centered at O. BC is tangent to the circle at B. If OP bisects the chord AD and $\angle A O P=60^{\circ}$, then find $m \angle C$.

Answer

$60^{\circ}$

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Question 181 Mark

Two concentric circles are of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

Answer

$2 \sqrt{a^2-b^2}$

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Question 191 Mark

In Fig. PA and PB are tangents to the circle with centre O such that $\angle A P B=50^{\circ}$. Write the measure of $\angle O A B$.

Answer

$25^{\circ}$

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Question 201 Mark

In Fig. CP and CQ are tangents from an external point C to a circle with centre O. AB is another tangent which touches the circle at R. If CP = 11 cm and BR = 4cm find the length of BC.
[Hint: Given, $CP=11 cm. \therefore CP = CQ \Rightarrow CQ=11 cm$. Tangents drawn point B are equal $\therefore \quad BR = BQ \Rightarrow B Q=4 cm$. Hence, $BC = CO - BQ = (11 - 4) cm = 7 cm$.

Answer

7 cm

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Question 211 Mark

In Fig.$\triangle A B C$ is circumscribing a circle. Find the length of BC.

Answer

10 cm

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Question 221 Mark

In Fig. CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 7 cm, then find the length of BR.

Answer

4 cm

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Question 231 Mark

What is the distance between two parallel tangents of a circle of radius 4 cm?

Answer

8 cm

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Question 241 Mark

In Q. No. 1, if PB = 10 cm, what is the perimeter of $\triangle P C D$?

Answer

20 cm

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Question 251 Mark

What the distance between two parallel tangents to a circle of radius 5 cm?

Answer

10 cm

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Question 261 Mark

The length of tangent from a point A at a distance of 5 cm from the centre of the circle is 4 cm. What is the radius of the circle?

Answer

3 cm

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Question 271 Mark

Two tangents TP and TQ are drawn from an external point T to a circle with centre O as shown in Fig. If they are inclined to each other at an angle of 100°, then what is the value of $\angle P O Q$?

Answer

$80^{\circ}$

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Question 281 Mark

In Fig. PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length PC?

Answer

8 cm

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1 Marks Question - MATHS STD 10 Questions - Vidyadip