Question

in the given figure AB=AC and O is the centre of the circle If angle BOA=90° determine angle AOC​

Answer 1

Answer : In triangle AOB and triangle AOC

AB=AC (given)

OB=OC (o is the center of the circle)

OA=OA (common side)

∆BOA=∆AOC (by SSS congruency rule)

Hence, angle AOC = 90° ( by CPCT )

Answer 2

Given - Angle BOA=90°

Find - Angle AOC

Solution - Let the angle AOC be x. Supplementary angles are the angles which sum up to 180°.

As the angles are supplementary angles, so the expression representing angles of concern will be -

AOC + BOA = 180

Keep the values in expression

AOC + 90 = 180

Shifting 90 to Right Hand Side

AOC = 180 - 90

Performing substraction

AOC = 90°

Hence, angle AOC is 90°