Question

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

Answer 1

REF.Image.

Let AB be a chord of a circle with center O and

let AR and BR

be the tangents

at A and B

Let the tangent meet at R. Join OR

and suppose OR meets AB at C.

To Prove : $\angle RAC=\angle RBC$

Proof : In $△RAC$ and $△RBC$

tangents from an external point

to a circle are equal

$\therefore RA=RB$

RA and RB are equally inclined to OR

$\therefore \angle ARC=\angle BRC$

$RC=RC$ (common in both triangles)

$△RAC\cong △RBC$ according to

SAS congruence

Hence proofes

$\therefore \angle RAC=\angle RBC$