Question

in the figure point b lies on a circle centered at point p, and (overline{ac}) is a diameter of the circle.
what is the measure of the minor arc (bc)?
○a (35^{circ})
○b (110^{circ})
○c (145^{circ})
○d (180^{circ})

Explanation:

Step1: Find the measure of ∠APB

Given that ∠APB = 35° (central angle).

Step2: Find the measure of ∠BPC

Since AC is a diameter, ∠APC = 180°.
We know that ∠APC=∠APB + ∠BPC.
Substituting the values, 180°=35° + ∠BPC.
Then ∠BPC=180° - 35° = 145°.

Answer:

C. 145°