Question

Prove that the tangents drawn at the end points of a chord of a circle make equal angles with the chord.

Answer 1

To prove `angle1=angle2`, let PQ be a chord of the circle. Tangents are drawn at the points R and Q.

Let P be another point on the circle, then join PQ and PR.
Since, at point Q there is a tangent.
`:.angle2=angleP` [angles in alternate segments are equal]
Since, at point R, there is a tangent.
`:.angle1=angleP`
[angles in alternate segments are equal]
`angle1=angle2=angleP` Hence proved.