Abcd Is Parallelogram Circle Through B And C Intersects Produce If Necessary At E
ABCD is a parallelogram. The circle through A, B and C intersects (produce if necessary) at E. Prove that AE =AD.
Given : ABCD is a parallelogram. Circle through A,B and C intersects CD produced in E.
To Prove : AE = AD
Proof : ABCE is a cyclic quadrilateral.
∴ ∠B + ∠E = 180° …i)
ABCD is a parallelogram .
∴ ∠B + ∠E = ∠B + ∠2
⇒ ∠E = ∠2
In △ADE, we have
∠E = ∠2
⇒ AD = AE [sides opposite to equal angles of a △]