Case study (4 Marks)

Question 14 Marks

Prem did an activity on tangents drawn to a circle from an external point using 2 straws and a nail for maths project as shown in figure.

Based on the above information, answer the following questions.

Number of tangents that can be drawn to a circle from an external point is:
On the basis of which of the following congruency criterion, $\triangle\text{OAP}\cong\triangle\text{OBP}?$
$\text{If }\angle\text{AOB}=150^\circ,\text{then }\angle\text{APB}=$
Or
$\text{If }\angle\text{APB}=40^\circ,\text{then }\angle\text{BAO}=$

Answer

1. 22. RHS
3. 30º
Or
20º

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Question 24 Marks

Following are questions of section-A in assessment test on circle that Eswar attend last month in school. He scored 5 out of 5 in this section. Answer the questions and check your score if I mark is allotted to each question.

A parallelogram circumscribing a circle is called a:
Is PQ a tangent to both the circles ?
Number of tangents that can be drawn to a circle from a point inside it, is:
Or
If l is a tangent to the circle with center O and line m is passing through O intersects the tangent l at point of contact, determine the answer:

Answer

1. Rhombus2. Yes
3. 0
Or
$\text{l }\bot\text{ m}$

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Question 34 Marks

In a park, four poles are standing at positions A, B, C and D around the fountain such that the cloth joining the poles AB, BC, CD and DA touches the fountain at P, Q, R and S respectively as shown in the figure.

Based on the above information, answer the following questions.

If O is the centre of the circular fountain, then $\angle\text{OSA}=$
Which of the following is correct?
If DR = 7cm and AD= 11cm, then AP =
Or
If O is the centre of the fountain, with $\angle\text{QCS}=60^\circ, \text{then }\angle\text{QOS}=$

Answer

1. 90º2. Since, length of tangents drawn from an external point to a circle are equal.
$\therefore$ AS = AP, BP = BQ,
CQ = CR and DR = DS
3. 4 cm
Or
120º

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Question 44 Marks

If a tangent is drawn to a circle from an external point, then the radius at the point of contact is perpendicular to the tangent. Answer the following questions using the above condition.

Two concentric circles are of radii 5cm and 3cm. Find the length of the chord of the larger circle which touches the smaller circle.
Two concentric circles are such that the difference between their radii is 4cm and the length of the chord of the larger circle which touches the smaller circle is 24cm. Then the radius of the smaller circle is:
In the given figure, O is the center of two concentric circles of radii 5cm and 3cm. From an external point P, tangents PA and PB are drawn to these circles. If PA = 12cm, then PB =

Or
In the given figure, O is the center of two concentric circles. From an external point P, tangents PA and PB are drawn to these circles, such that PA = 6cm and PB = 8cm. If OP = 10cm, then AB =

Answer

1. 8cm2. 16cm
3. $4\sqrt{10}\text{cm}$
Or
2cm

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Question 54 Marks

Smita always finds it confusing with the concepts of tangent and secant of a circle. But this time she has determined herself to get concepts easier. So, she started listing down the differences between tangent and secant of a circle, along with their relation. Here, some points in question form are listed by Smita in her notes. Try answering them to clear your concepts also.

A line that intersects a circle exactly at two points is called:
Number of tangents that can be drawn on a circle is:
Number of tangents that can be drawn to a circle from a point not on it, is:
Or
Number of secants that can be drawn to a circle from a point on it is:

Answer

1.Secant2. Infinite
3. 2
Or
Infinite

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Maths Case study (4 Marks)

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