Mathematics
In the adjoining figure, two chords AB and CD of a circle intersect at P. If AB = CD, prove that arc AD = arc CB.
Circles
22 Likes
Answer
Given AB = CD
Since, in a circle, equal chords cut off equal arcs.
∴ arc AB = arc CD
Subtracting arc BD from both sides we get,
⇒ arc AB - arc BD = arc CD - arc BD
⇒ arc AD = arc CB.
Hence, proved that arc AD = arc CB.
Answered By
15 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.
Prove that the angle subtended at the center of a circle is bisected by the radius passing through the mid-point of arc.