Question

Nagar BA is a tangent to the circle drawn from the external point P, and PVC is the second to the circle with BC as a diameter. If angle AOC is 130 degrees, then find the measure of angle APB, where O is the center of the circle.

a) 65 degrees
b) 80 degrees
c) 100 degrees
d) 130 degrees

Answer 1

To find the measure of angle APB, we can use the properties of tangents and circles. Angle APB is half of angle AOB, which can be found by subtracting angle AOC from 180 degrees.

Step-by-step explanation:

To find the measure of angle APB, we need to use some properties of tangents and circles. Let's start by drawing the diagram with the given information.

From the problem, we know that BA is a tangent to the circle at point A, and PVC is a diameter of the circle with B as the center. We also know that angle AOC is 130 degrees.

Based on the properties of tangents and circles, we can conclude that angle AOB is 90 degrees because it is formed by a tangent and a radius of the circle. Since angle AOC is 130 degrees, we can find angle BOC by subtracting 130 degrees from 180 degrees (180 - 130 = 50 degrees).

Now, to find angle APB, we can use the fact that angle APB is half of angle AOB. Therefore, angle APB is 90 degrees divided by 2, which is 45 degrees. So the answer is choice (d) 130 degrees.