Question

calculate ZEBC.
OD
In the given figure, O is the centre of a circle
in which ZOAB = 20° and ZOCB = 55°.
Find (i) ZBOC, (ii) ZAOC. [CBSE 2001C]​

Answer 1

Step-by-step explanation:

We know that BD=OD.

But OD=OB= Radius of the circle.

Therefore

BD=OD=OB

BDO is equilateral triangle.

Angle DBO= 60°

Now let us take the intersecting point of CD and AB as X.

In triangle BDX,

BXD= 90°(BXD+BXC=180°, BXD+90°=180°, BXD=90°)

BXD+DBX+BDX=180°{Angle Sum Property}

90°+60°+BDX= 180°

BDX= 30°

We also know that,

BDC(BDX)= BAC (Angles lie on the same arc{BC} are equal in measure.

Therefore,

BAC=BDC(BDX)=30°