Question

if a tangent of BA and PB from a point P of a circle with the centre O are inclined each other at 80 degree then find the angle p o a

Answer 1

Answer:

angle POA = 50

Step-by-step explanation:

tangents PA & PB are equal according to the theorem that two tangents drawn from an external point to a circle are equal.

and angle PAO = angle PBO = 90 according to the theorem that tangent is perpendicular to radius.

and angle APB = 80 (given)

using angle sum property of a quadrilateral,

PAO + PBO + AOB + APB = 360

90 + 90 + AOB + 80 = 360

AOB + 260 = 360

AOB = 100

In triangle PAO & triangle PBO

PA = PB  

OA = OB ( radii)

angle PAO = angle PBO = 90

therefoere, the 2 triangles are congruent ( RHS rule)

angle AOP = angle BOP  (cpct)

now,

angle AOP + angle BOP = angle AOB

angle AOP + angle AOP = 100   ( angle AOP = angle BOP)

2 angle AOP = 100

angle AOP = 50

therefore angle POA = 50