Question

if tangents pa and pb from a point p to a circle with center o are inclined to each other at an angle of 60°, them ∆poa is equal to​

Answer 1

Answer

500

Step-by-step explanation:

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Class 10

>>Maths

>>Circles

>>Tangent to a Circle

>>If tangents PA and PB from a point P to

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If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80

∘

, then ∠POA is equal to:

Medium

Solution

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Given that,

PA and PB are two tangents a circle and ∠APB=80

0

To find that ∠POA=?

Construction:- join OA,OBandOP

Proof:- Since OA⊥PA and OB⊥PB

Then ∠OAP=90

0

and ∠OBP=90

0

In

ΔOAP&ΔOBP

OA=OB(radius)

OP=OP(Common)

PA=PB(lengthsoftangentdrawnfromexternalpointisequal)

∴ΔOAP≅ΔOBP(SSScongruency)

So,

[∠OPA=∠OPB(byCPCT)]

So,

∠OPA=

2

1

∠APB

=

2

1

×80

0

=40

0

In ΔOPA,

∠POA+∠OPA+∠OAP=180

0

∠POA+40

0

+90

0

=180

0

∠POA+130

0

=180

0

∠POA=180

0

−130

0

∠POA=50

0

The value of ∠POA is 50

0

.