Question

In a circle with center O seg Op perpendicular chord AB,
AB=4cm, OP=7cm.
Then find radius of the circle?

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Answer 1

Taking triangle AOP and triangle POB, we get

AO=OB (radii of circle)

OP=OP (common side)

Angle APO = Angle OPB

Which implies that triangle OAP is congruent to triangle POB.

and thus AP=PB (CPCT)

In triangle AOP,

using Pythagoras theorem, we get

AP^2+OP^2=OA^2

(48/2)^2+(7^2)=OA^2

24^2+49=OA^2

576+49=OA^2

√625=OA

OA=25cm = radius of the circle.