ICSE Class 10th Mathematics Chapter 18 - Tangent and Intersecting Chords Important Questions with Answers

Radii of two circles are 6.3 cm and 3.6 cm. State the distance between their centres if:

1. they touch each other externally,
2. they touch each other internally.

From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that:

?AOP = ?BOP

From a point P outside a circle, with centre O, tangents PA and PB are drawn. Prove that:

OP is the ? bisector of chord AB.

In the given figure, two circles touch each other externally at point P. AB is the direct common tangent of these circles. Prove that :

1. tangent at point P bisects AB,
2. angles APB = 90°.

Tangents AP and AQ are drawn to a circle, with centre O, from an exterior point A. Prove that : ?PAQ = 2?OPQ

Two parallel tangents of a circle meet a third tangent at points P and Q. Prove that PQ subtends a right angle at the centre.

ABC is a right angles triangle with AB = 12 cm and AC = 13 cm. A circle, with centre O, has been inscribed inside the triangle.

Calculate the value of x, the radius of the inscribed circle.

In a triangle ABC, the incircle (centre O) touches BC, CA and AB at points P, Q and R respectively. Calculate : 

1. ?QOR
2. ?QPR;

given that ?A = 60°.

In the following figure, PQ and PR are tangents to the circle, with centre O. If `?`QPR = 60°, calculate:

1. ?QOR,
2. ?OQR,
3. ?QSR.

In the given figure, AB is the diameter of the circle, with centre O, and AT is the tangent. Calculate the numerical value of x.