INDIAN SCHOOL DARSAIT
DEPARTMENT OF MATHEMATICS
Subject : MATHEMATICS Topic : CIRCLES Date of Worksheet : 24/10/2019
Worksheet no:10
Resource Person:Mrs.Anu Likson
Name of the Student _______________ Class &Division:_______ Roll Number : ___
. Section A -[Chapter based questions] Marks
1. If AB , AC and PQ are tangents in the given figure and AB = 5cm , find the
perimeter of APQ. A
3
X
P Q
B C
2. If ABC is isosceles with AB = AC and C (O, r) is the incircle of the ABC 3
touching BC at L , prove that L bisects BC.
3. In the figure , AB is a chord of length 16 cm of a circle of radius 10 cm. The 4
tangents at A and B intersect at a point P. Find the length of PA.
A
P O
L
B
4. In the figure , there are two concentric circles with centre O of radii 5 cm and 3 cm. 2
From an external point P , tangents PA and PB are drawn to these circles. If
AP = 12 cm , find the length of BP.
A
P
O
5. Two tangents PA and PB are drawn to a circle with centre O such that 3
APB =1200. Prove that OP = 2AP.
6. In figure PA and PB are tangents drawn from an external point P to a circle with 4
centre O. LN touches the circle at M . Prove that PL + LM = PN + MN.
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INDIAN SCHOOL DARSAIT
DEPARTMENT OF MATHEMATICS
A
L
P
.O M
N
B
7. In figure , a circle touches all the four sides of a quadrilateral ABCD with AB = 6 4
cm , BC = 7cm and CD = 4 cm . Find AD.
R C
D
A P B
8. In the given figure OQ : PQ = 3 : 4 and perimeter of ∆POQ = 60 cm. Find the 4
length of PQ, QR and OP.
p Q
R
9. 4
In the given figure, a circle is inscribed in PQR with PQ = 10 cm, QR = 8 cm and
PR = 12 cm. Find the lengths of QM, RN and PL.
P
L
N N
Q
M
R
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