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 the respective points of contact, and ∠PAB = 55°. 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.
Points of contact are A and B, respectively.
∠PAB = 55º
Formula used:
In a triangle, the sum of all angles is 180º.
∠PAB + ∠ABP + ∠APB = 180º
Calculation:
Since the circles touch externally, ∠APB = 90º (property of tangents).
⇒ ∠PAB + ∠ABP + 90º = 180º
⇒ 55º + ∠ABP + 90º = 180º
⇒ ∠ABP = 180º - 145º
⇒ ∠ABP = 35º
∴ The correct answer is option (3).
Last updated on Dec 9, 2024
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