Question

AB is the chord of a circle with centreO. AB is produced to C, such that BC =OB, CO is joined and produced to meet the circle in D.
If `angle ACD=Y^@` and `angle AOD=x^@`, Prove that `x = 3y`.

Answer 1

Given : AB is a chord of a with centreO. Also, BO=BC.CO is joined produced to meet the circle at D.
To prove : `x=3y`
Proof : Since `BC=OB` (given)
`therefore angle OCB=angle BOC=Y^@` (angles opposite to equal sides are equal)
`thereforeangle ABO=angleBOC+angleOCB` (exterior angle circle)
`rArrangle ABO=y+y=2y`
Now, `OA=OB` (radii of same circle)
`therefore angle OAB=angleABO` (angles opposite to equal sidse are equal )
`2y`