Mathematics
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.
Circles
1 Like
Answer
We know that,
If two arcs are equal, they subtend equal angles at centre, thus they will also subtend equal angle at the circumference.
⇒ ∠CDA = ∠BAD
These angles are alternate interior angles formed by transversal AD with lines CD and AB.
⇒ AB ∥ CD.
Hence, proved that chord AB and chord CD are parallel.
Answered By
3 Likes
Related Questions
Prove that the angle subtended at the centre of a circle is bisected by the radius passing through the mid-point of the arc.
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.