Question

P is the midpoint of arc APB of a circle.prove that the tangent drawn at P will be parallel to the chord AB

Answer 1

here is ur answer see the pic

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Answer 2

Mid-point of an arc APB of the circle = P

Therefore, arc AP = arc PB

= AP =  PB  [In a circle if two arcs are equal then the corresponding chords are also equal.]

In ΔAPB

AP = PB (Proved)

∠APB= ∠ABP ( As equal sides have equal angles opposite) --- 1

Tangent of the circle DPE and PB is the chord.

Therefore,

∠DAP = ∠ABP  --- 2

From (1) and (2), -  

∠ABP = ∠DAP

Hence proved