Question

In the given figure o is the center of the circle ab is a chord. In triangle oAB. Show that angle OAB=angle OBA

Answer 1

In the ∆OAB,
It is given that OA=OB because AB is a chord and it's ends A and B are joined with center O.
So,
O is the center and OA=OB which are the radius of circle.
And,
As we know that,if two sides are equal in any triangle, then sure it's opposite angles also be equal by the property of isosceles triangle.
Hence,
OA=OB,
Angle OAB=AngleOBA.

Answer 2

In the circle
 AB is a chord given
 OA=OB (both are radius of the circle)
as we know that in a triangle if two sides are equal then their opposite angles will also be equal
Now in triangle OAB
OA=OB
therefore angleOBA = angleOAB   (opposite angles)  proved