Q1 of 47 Page 10

Prove that the line segment joining the points of contact of two parallel tangents to a circle is a diameter of the circle.

                                       
Given: l and m are the tangent to a circle such that l || m, intersecting at A and B respectively.
To prove: AB is a diameter of the circle.
Proof:
A tangent at any point of a circle is perpendicular to the radius through the point of contact.
∴ ∠ XAO = 90°
and ∠ YBO = 90°
Since ∠ XAO + ∠ YBO = 180°
Angles on the same side of the transversal is 180°.
Hence the line AB passes through the centre and is the diameter of the circle.

More from this chapter

All 47 →
2 Find the length of the tangent from a point which is at a distance of 5 cm from the centre of the circle of radius 3 cm. 3 Find the locus of centres of circles which touch a given line at a given point. 4 In two concentric circles, prove that all chords of the outer circle which touch the inner circle are of equal length. 5 Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.