Question

PQ and RS are two chords of a circle with centre O which intersect inside the circle at point

T. A and B are midpoints of the PQ and RS respectively. Show that O,A,T and B are

concyclic.​

Answer 1

Given : PQ and RS are two chords of a circle with centre O which intersect inside the circle at point T.

A and B are midpoints of the PQ and RS respectively.

To Find : Show that O,A,T and B are concyclic.​

Solution:

PQ is chord and A is mid point

=> OA ⊥ PQ    as perpendicular from center on chord bisect the chord

RS is chord and B is mid point

=> OB ⊥ RS    as perpendicular from center on chord bisect the chord

In Quadrilateral   OATB

∠A  = ∠B = 90°

∠A + ∠B = 90° + 90° = 180°

as Sum of opposite angles = 180°

Hence Quadrilateral   OATB is concyclic

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