Question
Download Solution PDFTwo circles touch each other externally at P. AB is a direct common tangent to the two circles, A and B are points of contact, and ∠PAB = 40° . The measure of ∠ABP is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Two circles touch each other externally at P.
AB is a direct common tangent to the two circles, A and B are points of contact, and ∠PAB = 40°.
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, ∠APB = 90°
Considering ΔAPB,
∠ABP
⇒ 90° - ∠PAB
⇒ 90° - 40° = 50°
∴ The measure of ∠ABP is 50°.
Last updated on Jun 2, 2025
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