Question : 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 $\angle$PAB = 22°. The measure of $\angle$ABP is:
Option 1: 72°
Option 2: 68°
Option 3: 70°
Option 4: 44°
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Correct Answer: 68°
Solution :
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, $\angle$APB = 90°
Considering $\triangle$APB,
$\angle$ABP = 90° – $\angle$PAB
$\therefore \angle$ABP = 90° – 22° = 68°
Hence, the correct answer is 68°.
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