Question

if tangents PA and PB from a point p to a circle with centre o are inclined to each other at an angle of 80 degrees then PO is equal to​

Answer 1

Question :

if tangents PA and PB from a point p to a circle with centre o are inclined to each other at an angle of 80 degrees then PO is equal to

Solution:

Given that,

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

To find that ∠POA=?

Construction:- join OA,OBandOP

Proof:- Since OA⊥PA and OB⊥PB

Then ∠OAP=90

and ∠OBP=90

In ΔOAP&ΔOBP

OA=OB(radius)

OP=OP(Common)

PA=PB(lengthsoftangentdrawnfromexternalpointisequal)

∴ΔOAP≅ΔOBP(SSScongruency)

So,

[∠OPA=∠OPB(byCPCT)]

So,

∠OPA= 1/2∠APB

=1/2 ×80

=40

In ΔOPA,

∠POA+∠OPA+∠OAP=180

∠POA+40+90=180

∠POA+130=180

∠POA=180−130

∠POA=50

The value of ∠POA is 50

More to know :

• The tangent to a circle is defined as a straight line which touches the circle at a single point.
• The point where the tangent touches a circle is known as the point of tangency or the point of contact