Question

for a circle with centre O two tangents PA and PB form an angle 180° from an external point P find m angle POA?​

Answer 1

Answer:

Given that,

PA and PB are two tangents a circle and ∠APB=800

To find that ∠POA=?

 Construction:- join OA,OBandOP

Proof:-  Since   OA⊥PA     and      OB⊥PB

Then    ∠OAP=900     and    ∠OBP=900

In 

ΔOAP&ΔOBP

OA=OB(radius)

OP=OP(Common)

PA=PB(lengthsoftangentdrawnfromexternalpointisequal)

∴ΔOAP≅ΔOBP(SSScongruency)

So,

[∠OPA=∠OPB(byCPCT)]

So,

∠OPA=21∠APB

                  =21×800=400

In    ΔOPA,

∠POA+∠OPA+∠OAP=1800

∠POA+400+900=1800

∠POA+1300=1800

∠POA=1800−1300

∠POA=500

The value of ∠POA is  500.