AB is a diameter of a circle with center O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62°, then find the measure of the minor arc AC.
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 56°
Here, Diameter AB is perpendicular to tangent AP
angle(BAP) = 90°
The angle subtended by the diameter on the circumference is 90°
angle(ACB) = 90°
angle(ACP) = 90° -------- (By Linear pair)
In tri(APC),
angle(PAC) + 90° + 62° = 180°
⇒ angle(PAC) = 28°
Now, angle(OAC) = 90° - 28° - 62°
Now, angle(OAC) = angle(OCA) = 62° -------(Angle opposite to equal side)
The measure of the minor arc (AC) = angle(AOC)
In tri(AOC)
angle(AOC) + 62° + 62° = 180°
⇒ angle(AOC) = 56°
The measure of the minor arc AC is 56°