PT is a tangent to a circle with center O at point C, and AB is the diameter. When BA is produced forward, it meets PT at point P. If ∠BPC = 34°, then what is the measure of ∠ACP?
Show answer & explanation
Correct answer: B
Explanation
Given:
PT is the tangent at point C.
OC is the radius ⇒ ∠OCP = 90°
∠BPC = 34°
AB is the diameter.
By formula:
Angle sum of a triangle = 180°
In an isosceles triangle, the base angles are equal.
Tangent-Chord Theorem
In ΔOCP
∠OCP = 90°
∠OPC = 34°
∠POC = 180° − 90° − 34° = 56°
Because B, O, A lie on the same straight line,
∠AOC = 56°
In ΔOAC
OA = OC
∠OCA = ∠OAC
∠OCA = (180° − 56°) / 2 = 62°
∠ACP = ∠OCP − ∠OCA = 90° − 62°= 28°