Class 10 CBSE Maths Circles Boards Questions
Here we provide Class 10 Maths important notes,board questions and predicted questions with Answers for chapter Circles. These important notes,board questions and predicted questions are based on CBSE board curriculum and correspond to the most recent Class 10 Maths syllabus. By practising these Class 10 materials, students will be able to quickly review all of the ideas covered in the chapter and prepare for the Class 10 Board examinations.
2016
Q1
In fig. 1, PQ is a tangent at a point C to a circle with centre O.
If AB is a diameter and ∠CAB = 30°, find ∠PCA.
solutions
solutions
Q2
In Fig.2, a quadrilateral ABCD is drawn to circumscribe a circle, with
centre O, in such a way that the sides AB, BC, CD and DA touch the circle at
the points P, Q, R and S respectively. Prove that. AB + CD = BC + DA.
solutions
solutions
Q3
In Fig. 3, from an external point P, two tangents PT and PS are drawn to a
circle with centre O and radius r. If OP = 2r, show that ∠OTS = ∠OST = 30°.
solutions
solutions
Q4
Prove that the lengths of the tangents drawn from an external point to a circle
are equal.
solutions
solutions
Q5
In Fig. 7, two equal circles, with centres O and O', touch each other at X.OO'
produced meets the circle with centre O' at A. AC is tangent to the circle with
centre O, at the point C. O'D is perpendicular to AC. Find the value of
DO'/CO
solutions
solutions
2017
Q1
If the angle between two tangents drawn from an external point P to a
circle of radius a and centre O, is 60°, then find the length of OP.
solutions
solutions
Q2
(1) Prove that the tangents drawn at the end points of a chord of a circle
make equal angles with the chord.
(2) A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA
solutions
(2) A circle touches all the four sides of a quadrilateral ABCD. Prove that AB + CD = BC + DA
solutions
Q3
Prove that the lengths of two tangents drawn from an external point to a
circle are equal.
solutions
solutions
Q4
In the given figure, XY and X' Y' are two parallel tangents to a circle with
centre O and another tangent AB with point of contact C, is intersecting
XY at A and X'Y' at B. Prove that ∠AOB = 90°.
solutions
solutions
2018
Q1
Prove that the lengths of tangents drawn from an external point to a circle are equal.
solutions
solutions
2019
Q1
In Figure 3, PQ and RS are two parallel tangents to a circle with centre O
and another tangent AB with point of contact C intersecting PQ at A and
RS at B. Prove that ∠AOB = 90°
solutions
solutions
2020
Q1
(1) In Fig. 1, A ABC is circumscribing a circle, the length of BC is ______ cm.
(2) In Fig. 3, two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2 ∠OPQ.
solutions
(2) In Fig. 3, two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2 ∠OPQ.
solutions
Q2
(1) In Fig. 1, on a circle of radius 7 cm, tangent PT is drawn from a point
P such that PT = 24 cm. If O is the centre of the circle, then the length of
PR is
(a) 30 cm
(b) 28 cm
(c) 32 cm
(d) 25 cm
(2) In Fig. 4, a circle touches all the four sides of a quadrilateral ABCD. If AB 6 cm, BC = 9 cm and CD = 8 cm, then find the length of AD.
solutions
(a) 30 cm
(b) 28 cm
(c) 32 cm
(d) 25 cm
(2) In Fig. 4, a circle touches all the four sides of a quadrilateral ABCD. If AB 6 cm, BC = 9 cm and CD = 8 cm, then find the length of AD.
solutions
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