Two circles touch each other externally at P. AB is a direct common tangent to the two circles. If A and B are points of contact and PAB = 65°, then ABP is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 25°.
Given:
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 = 65°
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°.
According to the concept, ∠APB = 90°
Considering ΔΑΡΒ,
⇒ ∠ABP = 90°- ∠PAB
⇒ 90°- 65° = 25°
So, ∠ABP = 25°