Question

Prove that the tangents at the extremities of any chord make equal angles with the chord.​

Answer 1

Answer:

HERE IS YOUR ANSWER DEAR

Step-by-step explanation:

let AB be a chord of a circle with centre O and let AP and BP be the tangents at A and B respectively .

Suppose the tangents meet at P.

Join OP

Suppose that OP meets AB at C

we gave to prove that angle PAC = angle PBC

In triangles PCA and PCB

PA=PB ( tangents from an external points are equal )

angle APC = angle BPC (PA and PB are equally inclined to OP )

and PC = PC (Common)

Thus by side angle side criterion of congruence

∆PAC ~= ∆ PBC ( by SAS )

the corresponding parts of the congruent triangles are congruent.

==== angle PAC = angle PBC ( by CPCT )

HENCE PROVED