wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In the given figure, AB is a chord of a circle with center O and AB is produced to C such that BC=OB. Also, CO is joined and produced to meet the circle in D. If ACD=yo and AOD=xo, prove that x=3y
1715476_e921a00e160843438b1ac2ad10bb0f38.png

Open in App
Solution

It is given that AB is a chord of a circle with centre O ans AB is produced to C such that BC=OB

We know that BOC and BCO form isosceles triangle

BOC=BCO=yo

We know that OA and OB are the radii of same circle

OA=OB

We know that OAB and OBA form isosceles triangle

OAB=OBA=2yo

From the figure we know that

Exterior AOD=OAC+ACO

It can be written as

Exterior AOD=OAB+BCO

So we get

Exterior AOD=3yo

It is given that

AOD=xo

So we get

xo=3yo

Therefore it is proved that x=3y

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Circles and Quadrilaterals - Cyclic quadrilaterals
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon