NCERT Class 10 Maths — Chapter 10

Exercise 10.1: Tangent to a Circle — Introduction

Understand the basic properties: a tangent touches the circle at exactly one point, and the radius to the point of tangency is perpendicular to the tangent.

tangentpoint of tangencytangent perpendicular to radius

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These questions cover the same concepts as Exercise 10.1. Try solving them to build confidence before or after the textbook exercise.

Which of the following statements about tangents to a circle is INCORRECT?

A.A) A tangent to a circle intersects the circle at exactly one point.

B.B) The tangent at any point of a circle is perpendicular to the radius through the point of contact.

C.C) The lengths of tangents drawn from an external point to a circle are equal.

D.D) The line segment joining the points of contact of two parallel tangents to a circle is always a radius.

A quadrilateral ABCD is drawn to circumscribe a circle. If AB = 8 cm, BC = 7 cm, and CD = 6 cm, then the length of AD is:

A.5 cm

B.7 cm

C.9 cm

D.11 cm

A circle is inscribed in a triangle ABC, touching sides AB, BC, and AC at points P, Q, and R respectively. If AB = 12 cm, BC = 8 cm, and AC = 10 cm, what is the length of AP?

A.5 cm

B.6 cm

C.7 cm

D.8 cm

A student states that if a line AB is tangent to a circle at point P, and OP is a radius, then ∠OPA must be 60°. What is the error in this statement?

A.The angle should be 45°.

B.The angle should be 180°.

C.The angle should be 90°.

D.There is no error, the statement is correct.

Which of the following statements about tangents to a circle is INCORRECT?

A.A tangent to a circle intersects the circle at exactly one point.

B.The tangent at any point of a circle is perpendicular to the radius through the point of contact.

C.The lengths of tangents drawn from an external point to a circle are equal.

D.If a line intersects a circle at two points, it is called a tangent.

A line is drawn through the end-point of a radius of a circle and is perpendicular to it. What can be concluded about this line?

A.It must be a secant.

B.It must pass through the center.

C.It must be a tangent.

D.It must be a chord.

Two tangents PA and PB are drawn from an external point P to a circle with centre O. If the angle subtended by the chord of contact AB at the centre is 90°, what is the measure of the angle between the tangents, ∠APB?

A.60°

B.75°

C.80°

D.90°

Two circles with radii 5 cm and 3 cm touch each other externally. A common tangent PQ is drawn to the circles, where P and Q are points of contact. What is the length of PQ?

A.4√10 cm

B.2√10 cm

C.4√15 cm

D.2√15 cm

Which of the following statements correctly defines a tangent to a circle?

A.A line that intersects a circle at two points.

B.A line that passes through the center of a circle.

C.A line that touches a circle at exactly one point.

D.A line segment that connects two points on a circle.

Two circles with centres O and O' and radii 1 cm and 7 cm respectively, touch externally. A common tangent AB touches the circles at A and B respectively. Find the length of AB.

A.2√3 cm

B.2√7 cm

C.7 cm

D.12 cm

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