Mathematics
Prove that the angle subtended at the center of a circle is bisected by the radius passing through the mid-point of arc.
Circles
51 Likes
Answer
The figure of the circle is shown below:
Let C be the mid-point of arc AB.
∴ AC = BC.
Since, equal arcs subtend equal angles at center.
∴ ∠AOC = ∠BOC.
Hence, proved that ∠AOC = ∠BOC.
Answered By
40 Likes
Related Questions
If arcs APB and CQD of a circle are congruent, then find the ratio of AB : CD.
A and B are points on a circle with center O. C is a point on the circle such that OC bisects ∠AOB, prove that OC bisects the arc AB.
In the adjoining figure, two chords AB and CD of a circle intersect at P. If AB = CD, prove that arc AD = arc CB.
If P and Q are any two points on a circle, then the line segment PQ is called a
radius of the circle
diameter of the circle
chord of the circle
secant of the circle.