Question
Download Solution PDFTwo 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF
Given:
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°.
Concept used:
If two circles touch each other externally at some point and a direct common tangent is drawn to both circles, the angle subtended by the direct common tangent at the point where two circles touch each other is 90°.
Calculation:
According to the concept, ∠PMQ = 90°
Considering ΔPMQ,
∠MQP
⇒ 90° - ∠MPQ
⇒ 90° - 38° = 52°
∴ The measure of ∠MQP is 52°.
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