Angle subtended by an arc

Transcript

Angle subtended by an arc A part of a circle is called an arc Now, Major arc is greater than half of a circle. Eg: arc AYB Minor arc is smaller than half of a circle. Eg: arc AXB And, the angle which the subtend in the center is Angle subtended by arc in the center Now, we have a theorem Theorem 9: The angle subtended by an arc at the centre of the circle is double the angle subtended by the arc at any point on the circle outside the arc. Here, Angle subtended by arc AB at center = ∠ AOB = 90° Angle subtended by arc AB at point P on circle = ∠ APB = 35° Since 90° = 2 × 45° We can say that Angle subtended by arc at center is double the angle subtended at any other point on the circle Let’s look at the proof Major arc is greater than half of a circle. Eg: arc AYB Minor arc is smaller than half of a circle. Eg: arc AXB And, the angle which the subtend in the center is Angle subtended by arc in the center Since 90° = 2 × 45° We can say that Angle subtended by arc at center is double the angle subtended at any other point on the circle Let’s look at the proof Proof is here Theorem 9 of Chapter 5 Class 9 – Ganita Manjari Part 1 We get some interesting results from this Theorem