The Total solution for NCERT class 6-12
ABCD is a parallelogram. The circle through A, B and C intersect CD(produced if necessary) at E. Prove that AE, = AD.
Here, ABCE is a cyclicquadrilateral. In a cyclic quadrilateral, the sum of the opposite angles is180°.
So, ∠AEC+∠CBA = 180°
As ∠AEC and ∠AED are linear pair,
∠AEC+∠AED = 180°
Or, ∠AED = ∠CBA … (1)
We know in aparallelogram; opposite angles are equal.
So, ∠ADE = ∠CBA … (2)
Now, from equations(1) and (2) we get,
∠AED = ∠ADE
Now, AD and AE areangles opposite to equal sides of a triangle,