Question

33. The tangents PA and PB drawn from point P to a circle with centre O have tangent points A and B
respectively. If angle APB = 50° and angle OAB = 30° the find angle ABP​

Answer 1

Step-by-step explanation:

angle OAP = 90° (Tangent is perpendicular to the radius at the point of intersection)

but angle OAP = angle OAB + angle BAP

=> 90° = 30° + angle BAP

=> angle BAP = 90-30 = 60°

angle BAP + angle ABP + angle APB = 180° (angle sum property)

=> 60° + angle ABP + 50° = 180°

So, angle ABP = 180- 110° = 70°

However the question is wrong because the Tangents from same points are equal and angles opposite to same sides are also equal,

Hence angle ABP = angle BAP = 60°

As different answers are coming, the values given in the question are wrong.

Either angle APB should be 60° or angle OAB should be 25°