Two circles touch each other externally at M. PQ is a direct common tangent to the two circles, P and Q are points of contact and ∠MPQ = 38°. ∠MQP is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 52°.
According to the given question,
When two circles intersect externally and a common tangent is drawn touching both the circles, then the angle subtended by the tangents to the point of intersection of two circles is 90°.
In the figure above, ∠PMQ = 90°
∠MPQ = 38° (Given)
Then by using angle sum in triangle MPQ,
∠MPQ + ∠PMQ + ∠MQP = 180°
⇒ 38° + 90° + ∠MQP = 180°
∠MQP + 128° = 180°
∠MQP = 180° - 128°
∠MQP = 52°
Hence the value of ∠MQP is 52°.