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UNIT TEST

Unit test · Ch 10: Circles

20marks
11questions
60%to pass
4checks left

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Series RTEQ.P. Code 74/-3/-1
Roll No.

RTE LEARN · CBSE PATTERN 2026–27

MATHEMATICS

Unit test · Ch 10: Circles

Time allowed : 40 MinutesMaximum Marks : 20

General Instructions :

Read the following instructions carefully and follow them :

(i)This question paper contains 11 questions. All questions are compulsory.
(ii)This question paper is divided into three sections – A, B and C.
(iii)In Section A, Question numbers 1 to 5 carry 1 mark each.
(iv)In Section B, Question numbers 6 to 8 are very short answer (VSA) type questions carrying 02 marks each.
(v)In Section C, Question numbers 9 to 11 are short answer (SA) type questions carrying 03 marks each.
(vi)Draw neat figures wherever required. Take π = 22/7 wherever required, if not stated.
(vii)Use of calculators is not allowed.

SECTION A

This section comprises 5 questions of 1 mark each.

1.
A tangent PT is drawn from a point P at a distance of 10 cm from the centre of a circle of radius 6 cm. Find the length PT.
1
2.
Tangents PA and PB are drawn from an external point P to a circle. If PA = 8 cm, find PB.
1
3.
How many tangents can be drawn to a circle from a point lying inside it?
1
4.
What is the angle between a tangent to a circle and the radius drawn to the point of contact?
1
5.
How many points does a tangent to a circle have in common with the circle?
1

SECTION B

This section comprises 3 very short answer (VSA) type questions of 2 marks each.

6.
Two concentric circles have radii 10 cm and 6 cm. Find the length of the chord of the larger circle which touches the smaller circle.
2
7.
Tangents PA and PB from an external point P touch a circle at A and B. If ∠APB = 80°, find ∠PAB.
2
8.
A tangent PQ at a point P of a circle of radius 9 cm meets the line through the centre O at Q, where OQ = 41 cm. Find PQ.
2

SECTION C

This section comprises 3 short answer (SA) type questions of 3 marks each.

9.
Two tangents are drawn from a point P at a distance of 13 cm from the centre O of a circle of radius 5 cm, touching it at A and B. Find the length of the chord AB.
3
10.
A circle is inscribed in triangle ABC and touches BC, CA, AB at D, E, F. If AB = 9 cm, BC = 10 cm and CA = 11 cm, find AF, BD and CE.
3
11.
Prove that the lengths of the two tangents drawn from an external point to a circle are equal.
3

✦ ✦ ✦

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An example of what the app shows after checking. Each answer gets step marks and a short comment:

Q6 · 2/2Full marks. Correct method and the final answer is clearly stated.
Q7 · 1/2Right approach, but one step of working is missing. Show every step to get full marks.
Q8 · 2/2Well explained, with correct units and a neat diagram.
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