A circle is centered at P with radii PA¯¯¯¯¯¯¯¯ and PB¯¯¯¯¯¯¯¯ drawn such that the m∠APB=133° . AC←→ and BC←→ are drawn tangent to the circle at points A and B, respectively. What is the m∠ACB ?
A. m∠ACB=133°
B. m∠ACB=47°
C. m∠ACB=66.5°
D. m∠ACB=90°
C. m∠ACB=66.5°
Since ∠APB is an inscribed angle, its measure is half of the central angle subtended by AB. Thus, the central angle is 266°.
The measure of the angle formed by two tangents drawn from an external point to a circle is half the central angle, so m∠ACB = 266°/2 = 133°/2 = 66.5°. So, option C is correct.