Question

P,Q,R and S are points on the circumference of a circle. Work out the size of angle PSR. Give a reason for your answer.

Answer 1

To find the size of angle PSR, use the formula for an angle subtended by an arc on the circumference of a circle. Calculate the arc length PS and divide it by the circumference of the circle.

Step-by-step explanation:

To find the size of angle PSR, we need to know the positions of points P, Q, R, and S on the circumference of the circle. If we assume that P is the starting point and Q, R, and S are sequentially positioned on the circumference in a clockwise direction, we can determine the size of angle PSR. Since PSR is an angle subtended by an arc, we can use the formula for finding the measure of an angle subtended by an arc on the circumference of a circle. The formula is given by:

Angle = (Arc Length / Circumference) * 360 degrees

We can calculate the arc length PS and divide it by the circumference of the circle, which is 2πr (where r is the radius). Let's assume that the length of arc PS is a. The angle PSR can be calculated using the formula:

PSR = (a / 2πr) * 360 degrees

This will give us the measure of angle PSR in degrees.