Question

Prove that bisector of two parallel chords passes through the centre of circle.​

Answer 1

Answer:

Let us support PQ does not pass through O.

Let us support PQ does not pass through O.Since PQ⊥ bisector of AB

Let us support PQ does not pass through O.Since PQ⊥ bisector of AB∠QOP=90°⟶(1)

Let us support PQ does not pass through O.Since PQ⊥ bisector of AB∠QOP=90°⟶(1) P is the mid-point of AB.

Let us support PQ does not pass through O.Since PQ⊥ bisector of AB∠QOP=90°⟶(1) P is the mid-point of AB.QP passes through center from this, we can say

Let us support PQ does not pass through O.Since PQ⊥ bisector of AB∠QOP=90°⟶(1) P is the mid-point of AB.QP passes through center from this, we can sayOP⊥AB∠OPA=90°

Let us support PQ does not pass through O.Since PQ⊥ bisector of AB∠QOP=90°⟶(1) P is the mid-point of AB.QP passes through center from this, we can sayOP⊥AB∠OPA=90°Comparing 1 & 2, we can say

Let us support PQ does not pass through O.Since PQ⊥ bisector of AB∠QOP=90°⟶(1) P is the mid-point of AB.QP passes through center from this, we can sayOP⊥AB∠OPA=90°Comparing 1 & 2, we can say∴∠QOP=∠OPA, this can be possible only when O,P and Q are on the same line.

Let us support PQ does not pass through O.Since PQ⊥ bisector of AB∠QOP=90°⟶(1) P is the mid-point of AB.QP passes through center from this, we can sayOP⊥AB∠OPA=90°Comparing 1 & 2, we can say∴∠QOP=∠OPA, this can be possible only when O,P and Q are on the same line.∴ It is a contradiction PQ passes through O.