Question

(b) Prove that the tangents drawn from an external point
of circle make equal angles with line joining centre and external point . in figure , angle AOB = 100 degree find angle APO
​

Answer 1

Step-by-step explanation:

A circle with centre O and a point P outside it.

PA and PB are @ tangents to circle

To prove:

∠AOP=∠BOP

and,∠APO=∠BPO

Proof:

In ΔAOPandΔBOP

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

OA=OB (radii of same circle )

ΔAOP≅ΔBOP(SSS)

∴∠AOP=∠BOP

and∠APO=∠BPO(CPCT)

This is the right answer for your question.