LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
40 views
in Mathematics by (97.1k points)
closed by
ABCD is a parallelogram . The circle passing through the vertices. A, B and C intersects CD (or CD produced) at E. Prove that `AE=AD`.

1 Answer

0 votes
by (88.7k points)
selected by
 
Best answer
`angle1 +angle4 =180^@` (L.P.A.) ......(1)
`angle 2+angle3 =180^@` ........(2)
(sum of opposite of a cyclic quadrilateral is `180^@`)
`therefore` From (1) and (2), we get
`angle1 +angle4 =angle2 +anlge3` ......(3)
But (opposite angles of a parallelogram )
`therefore` From (3) and (4) ,
`angle1 +angle4 =angle2 +angle4`
`rArrangle1 =angle2`
`rArrAE=AD" "(because" sides opposite to equal angles are equal")`
image

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...