Mathematics
Prove that the angle subtended at the centre of a circle is bisected by the radius passing through the mid-point of the arc.
Circles
1 Like
Answer
Let C be the mid-point of arc AB.
∴ AC = BC.
Since, equal arcs subtend equal angles at center.
∴ ∠AOC = ∠BOC.
Hence, proved that the angle subtended at the centre of a circle is bisected by the radius passing through the mid-point of the arc.
Answered By
1 Like
Related Questions
In the given figure, arc AC and arc BD are two equal arcs of a circle. Prove that chord AB and chord CD are parallel.
In the given figure, P is the mid-point of arc APB and M is the mid-point of chord AB of a circle with centre O. Prove that:
(i) PM ⟂ AB
(ii) PM produced will pass through the centre O
(iii) PM produced will bisect the major arc AB.
Prove that in a cyclic trapezium, the non-parallel sides are equal.
If P is a point on a circle with centre O. If P is equidistant from the two radii OA and OB, prove that arc AP = arc PB.