Question

if tangent pa and pb from point p to circle with center o are inclined to each ohter at angle of 80°.find <poa=?

Answer 1

Answer:

Given-PA and PB are tangents & angle APB= 80 degree

To find- Angle POA

Construction- Join OA,OB & OP

Proof-

Since PA is tangent

OA is perpendicular to PA (Tangent at any point of circle is perpendicular to       the radius through point of contact)

Therefore angle OAP is equal to 90 Degree

In triangle OAP and triangle OBP

OA=OB (Radii of the circle)

PA=PB (Length of tangents drawn from an external point are equal)

OP=OP (common)

therefore Triangle OAP and OBP are congruent

so angle OPA=angle OPB (CPCT)

so angle OPA=1/2 of angle APB=1/2 x 80=40 degree

In triangle OPA-

angle POA+angle OPA+ angle OAP= 180 degree (angle sum property)

Angle POA+40 degree+90 degree=180 degree

Angle  POA=180 Degree-130 Degree

Angle POA=50 degree

Step-by-step explanation: