Question

pls help me...........how to do it​

Answer 1

Answer:

Step-by-step explanation:

Const :- Join OC

Proof :-

In ΔOPA and ΔOAC

OP = OC ( Radii )

AP = AC ( Tangent from external point are equal )

OA = AO ( Commom )

So Δ AOP ≅ ΔAOC

By CPST, <OAP = <OAC ∴ <OAC = 1/2 <A ........ i

Similarly, <OBQ = <OBC ∴ <OBC = 1/2 <B.......... ii

INΔ AOB,

<OAC + <AOB + <OBC = 180 ( ANGLE SUM PROPERTY )

<A/2 + <B/2 + <AOB = 180 ( By i and ii )

180/2 + <AOB = 180 ( Since <a and <b are cointerior angles due to parallel lines )

∴ <AOB = 90°

Hence Proved

Thank u

Hare Krsna