The given figure shows a circle with centre O. P is mid-point of chord AB.

Show that OP is perpendicular to AB.

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Solution

e draw line OA and OB .

In ∆OPA and ∆ OPB

OA = OB ( Radius of circle )
OP = OP ( Common side )
AP = PB ( Given )

∴∴ΔOPA ≅Δ OPB ( By SSS rule )
So,
∠ OPA = ∠OPB ------------- ( 1 )
And
we know
∠ OPA + ∠ OPB = 180° ( angle on same straight line )
So,
∠ OPA = ∠ OPB = 90° ( By equation 1 )
Hence
OP perpendicular to AB ( Hence proved )

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The given figure shows a circle with centre O. P is mid-point of chord AB. Show that OP is perpendicular to AB.

The given figure shows a circle with centre O. P is mid-point of chord AB.

Show that OP is perpendicular to AB.