# ABCD is a parlellogram.The circle through A,Band C intersect CD at E . Prove that AE = AD

2
Log in to add a comment

Log in to add a comment

a circle through A,B,C intesects CD produced at E

TO PROVE- AE=AD

PROOF- angle ADE +

a circle through A,B,C intesects CD produced at E

TO PROVE- AE=AD

PROOF- angle ADE +angle ABC =180 ........1 (sum of opp. angle of a cyclic qurd.)

angle ADE +angle ADC=180 ...........2 (LINEAR PAIR)

angle ABC = angle ADC=180 .......3 (opp. angle of a parallogram are equal)

from 1 and 2

angle ADE +angle ADC = angle ABC = angle ADC

angle AED = angle ADE (using 3)

In triangle AED,

angle AED = angle ADE

AE = AD (equal sides

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

I think the proof is that AE = BD, AD = BE. There is a mistake in the given question.

See the diagram.

ABCD is a parallelogram. The circumcircle through A,B, & C intersects extended CD in E.

We know that in a circle, a chord inscribes the same angle at any point on the circumference on the same side.

Let angle AED = x. Let angle DAE = y and let angle ADB = z.

Compare the triangles ADE and BDE.

DE is the common side. angle BDE = angle AED. angle DAE = angle DBE.

So the triangles are similar and as one side is common, the triangles are congruent.

* Hence, AD = BE and AE = BD*

Since, AD = BC,* AD = BE = BC.*

See the diagram.

ABCD is a parallelogram. The circumcircle through A,B, & C intersects extended CD in E.

We know that in a circle, a chord inscribes the same angle at any point on the circumference on the same side.

Let angle AED = x. Let angle DAE = y and let angle ADB = z.

Compare the triangles ADE and BDE.

DE is the common side. angle BDE = angle AED. angle DAE = angle DBE.

So the triangles are similar and as one side is common, the triangles are congruent.

Since, AD = BC,