AB is diameter of a circle with centre O if PA is tangent from an external point P to - Maths - Circles

Question

AB is diameter of a circle with centre O if PA is tangent from an
external point P to the circle with angle POB = 115 degrees then
find angle OPA

Varun.Rawat · Accepted Answer

We have AB as the diameter of the circle and O is the centre of the circle
Now, PA is tangent to the circle at A
We know that tangent to the circle is always ⊥ to the radius at the point of contact, so∠OAP = 90°
Now, ∠POB and ∠POA form a linear pair, then∠POB + ∠POA = 180°⇒115° + ∠POA = 180°⇒∠POA = 65°In ∆OAP, ∠OPA + ∠OAP + ∠POA = 180°   Angle sum property⇒∠OPA + 90° + 65° = 180°⇒∠OPA  + 155° = 180°⇒∠OPA  = 180° - 155° = 25°

AB is diameter of a circle with centre O. if PA is tangent from an external point P to the circle with angle POB = 115 degrees then find angle OPA