Question

Hi
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Please tell me answer of this question with step by step explanation☺️☺️​

Answer 1

Given= angle AOP=60

angle OAP=?

As p is the mid point of chord AB and OP is the distance of chord from the centre.

So angle OPA= 90

Now,

By internal angle sum property.

In triangle OAP

90+ 60 + angle OAP=180

150+ angle OAP = 180

angle OAP = 180-150

angle OAP = 30

hope it may help you.

please mark as a brainliest

Answer 2

Given: AB is the chord to the circle with
centre O
AP=PB
ANGLE AOP=60°

To Find: ANGLE OAP=?

Construction: Join OB

Solution: In ΔOAP & ΔOBP
S | OA=OB(radii of the circle)
S | AP=PB(given)
S | OP=OP(common)

therefore ΔOAP is congruent to ΔOBP(By SSS congruency criteria)

ANGLE OAP=ANGLE OBP(C.P.C.T.)
ANGLE AOP=ANGLE BOP(C.P.C.T.)

hence, ΔOAP & ΔOBP are equilateral Δ's

Angle AOP=Angle OPA=Angle OAP=60°

Thanks
Hope it helps you................