ac is tangent to circle o at point a, and mab = 59. what is m∠acb? (not drawn to scale) a 121 b 21 c 31 d 29
ac is tangent to circle o at point a, and mab = 59. what is m∠acb? (not drawn to scale) a 121 b 21 c 31 d 29
Answer
Explanation:
Step1: Recall tangent - arc relationship
The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.
Step2: Apply the formula
We know that $\angle ACB$ is the angle formed by tangent $\overline{AC}$ and chord $\overline{AB}$. The intercepted arc is $\overset{\frown}{AB}$ with $m\overset{\frown}{AB}=59$. So, $m\angle ACB=\frac{1}{2}m\overset{\frown}{AB}$.
Step3: Calculate the angle measure
$m\angle ACB=\frac{1}{2}\times59 = 29.5\approx29$ (rounding to the nearest whole - number as per the multiple - choice options).
Answer:
D. 29