A B C D is a cyclic quadrilateral. A Ba ...

`A B C D` is a cyclic quadrilateral. `A Ba n dD C` are produced to meet in `Edot` Prove that `E B CcongE D A dot`

Text Solution

Verified by Experts

Solution:
Given
`ABCD` is a cyclic quadilateral and `AB` and `DC` are produced to meet at `E`
proof:
In `/_\ EBC and /_\EDA`
`/_EBC=/_EDA`(enterior angle in a cyclic quadilateral is equal to the opposite interial angle)
`/_E=/_E`(comman)
`/_ECB=/_EDA`(exterial angle in a cyclic quadilateral is equal to the opposite of interial angle)
`:. /_\EBC~=/_\EDA`(by AAA rule).

Topper's Solved these Questions

AREA OF PARALLELOGRAMS AND TRIANGLES
RD SHARMA|Exercise All Questions|205 Videos
CONGRUENT TRIANGLE
RD SHARMA|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

A B C D is a cyclic quadrilateral. A Ba n dD C are produced to meet in Edot Prove that E B C-E D Adot

ABCD is a cyclic quadrilateral in which BA and CD when produced meet in E and EA=ED. Prove that: ADBC( ii) EB=EC

A B C D is a cyclic quadrilateral whose diagonals A C\ a n d\ B D intersect at Pdot If A B=D C , prove that: P A B\ ~= P D C P A=P D\ a n d\ P C=P B (iii) A D B C

A B C D is a cyclic quadrilateral whose diagonals A Ca n dB D intersect at P . If A B=D C , Prove that : P A B~= P D C P A=P Da n dP C=P B A D B C

Ina cyclic quadrilateral angle A + angle C = angle B + angle D = ?

If ABCD is a cyclic quadrilateral in which ADBC( In figure).Prove that /_B=/_C

A B C D is a parallelogram. A D is a produced to E so that D E=D C and E C produced meets A B produced in Fdot Prove that B F=B Cdot

The diagonals of quadrilateral A B C D , A C a n d B D intersect in Odot Prove that if B O=O D , the triangles A B C a n d A D C are equal in area.

A B C D is a quadrilateral. A line through D , parallel to A C , meets B C produced in P as shown in Figure. Prove that a r\ ( A B P)=a r\ (Q u a ddotA B C D)dot

Any point D is taken in the base B C of a triangle A B C\ a n d\ A D is produced to E , making D E equal to A Ddot Show that a r\ ( B C E)=a r( A B C)

RD SHARMA-CIRCLE -All Questions

D\ a n d\ E are points on equal sides A B\ a n d\ A C of an isosce...
Text Solution
|
D\ a n d\ E are, respectively, the points on equal sides A B\ a n d\...
Text Solution
|
A B C D is a cyclic quadrilateral. A Ba n dD C are produced to meet in...
Text Solution
|
In an isosceles triangle A B C with A B=A C , a circle passing thr...
Text Solution
|
In Figure, /A=60^0\ a n d\ /A B C=80^0, find /D P C\ a n d\ /B Q C
Text Solution
|
In Figure, A B is a diameter of a circle C(O ,\ r)dot Chord C D is ...
Text Solution
|
P Q\ a n d\ R S are two parallel chords of a circle and lines R P\ a...
Text Solution
|
A B C D is a cyclic quadrilateral whose diagonals A C\ a n d\ B D in...
Text Solution
|
P is a point on the side B C of a triangle A B C such that A B=A P...
Text Solution
|
A B C is a triangle in which A B=A C\ a n d\ P is a point on A C ....
Text Solution
|
In any triangle ABC, if the angle bisector of /Aand perpendicular bis...
Text Solution
|
Let the vertex of an angle ABC be located outside a circle and let t...
Text Solution
|
In Figure, A B C is an equilateral triangle. Find m\ /B E C
Text Solution
|
In Figure, P Q R is an isosceles triangle with P Q=P R\ a n d\ m/P...
Text Solution
|
In Figure, O is the centre of the circle. If /B O D=160^0, find the ...
Text Solution
|
In Figure A B C D is a cyclic quadrilateral. If /B C D=100^0a n d\ /A ...
Text Solution
|
If A B C D is a cyclic quadrilateral in which AD|\|BC . Prove that /...
Text Solution
|
In Figure, O is the centre of the circle. Find /C B D
Text Solution
|
A B\ a n d\ C D are diameters of a circle with centre Odot If /O B D...
Text Solution
|
On a semi-circle with A B as diameter, a point C is taken, so th...
Text Solution
|