#### Question

In the given figure, if arc AB = arc CD, then prove that the quadrilateral ABCD is an isosceles– trapezium (O is the centre of the circle).

#### Solution

Given –

In the figure, O is the centre of a circle and arc AB = arc CD

To prove –

ABCD is an isosceles trapezium.

Construction – Join BD, AD and BC.

Proof – Since equal arcs subtends equal angles at the circumference of a circle.

∴ ∠ADB = ∠DBC [∵ arc AB = arc CD]

But, these are alternate angles.

∴ AD|| BC

∴ ABCD is a trapezium

∵ Arc AB = Arc CD [Given]

∴ Chord AB = Chord CD

∴ ABCD is an isosceles trapezium

Is there an error in this question or solution?

Solution In the Given Figure, If Arc Ab = Arc Cd, Then Prove that the Quadrilateral Abcd is an Isosceles– Trapezium (O is the Centre of the Circle). Concept: Concept of Circles.