Question

2. Draw op perpendicular Ab at a,p,b
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Answer 1

$[]\huge \mathfrak\red {Ans}\mathfrak\pink{wer}$Given ; In the figure , O is center of the circle , and AB is chord . P is a point on AB such that AP = PB

We need to prove that AP = BP

Construction ; Join OA and OB

Proof ;

In right triangles ΔOAPandΔOBP

Hypotenuse OA = OB [radii of the same circle]

Side OP = Op [Common]

By Right angle - Hypotenuse - Side criterion of congruency ,

ΔOAP≅ΔOBP

the corresponding parts of the congruent triangles are congruent ,

AP = BP

Hence proved