Question

In the figure, P is the midpoint of chord AB. O is a centre of the circle measure angle AOP is equal to 60 degree then find measure angle OAP. Justify your steps.
please give me answer step by step ​

Answer 1

OP will perpendicular on AB.... a line drawn from center of the circle to its chord is perpendicular to a chord theorem.

Thefore angle OPA = 90° ... eqn 1

thefore in ∆ OPA

angle OPA = 180° - angle OPA ... sum of all angles of triangle.

therefore angle OPA = 180° - 90 ... from eqn 1

angle OPA = 60°

Answer 2

Answer:

Point O is the centre of the circle ,

measure angle AOP=90°

=measure angle OPA=90°(Perpendicular drawn from the centre of the circle bisects the chord)

=measure angle P=90°

=measure angle AOP+measure angle OPA+measure angle OAP=180°

=60+90+measure angle 0AP =180°

=measure angle OAP=180°-150°

=measure angle OAP=30°

therefore, measure angle OAP=30°