Question

TWO circles intersect each other at P and Q from diameter PA and PB are drawn to the two circles show that A,Q and B are co leaner.



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Answer 1

Let O and ' O be the centres of two intersecting circle, where

Let O and ' O be the centres of two intersecting circle, wherePoints of intersection are P and Q and PA and PB are their diameter respectively.

Let O and ' O be the centres of two intersecting circle, wherePoints of intersection are P and Q and PA and PB are their diameter respectively.Join PQ, AQ and QB.

Let O and ' O be the centres of two intersecting circle, wherePoints of intersection are P and Q and PA and PB are their diameter respectively.Join PQ, AQ and QB.∴ ∠AQP = 90° and ∠BQP = 90°

Let O and ' O be the centres of two intersecting circle, wherePoints of intersection are P and Q and PA and PB are their diameter respectively.Join PQ, AQ and QB.∴ ∠AQP = 90° and ∠BQP = 90°(Angle in a semicircle is a right angle)

Let O and ' O be the centres of two intersecting circle, wherePoints of intersection are P and Q and PA and PB are their diameter respectively.Join PQ, AQ and QB.∴ ∠AQP = 90° and ∠BQP = 90°(Angle in a semicircle is a right angle)Adding both these angles,

Let O and ' O be the centres of two intersecting circle, wherePoints of intersection are P and Q and PA and PB are their diameter respectively.Join PQ, AQ and QB.∴ ∠AQP = 90° and ∠BQP = 90°(Angle in a semicircle is a right angle)Adding both these angles,∠AQP + ∠BQP = 180°

Let O and ' O be the centres of two intersecting circle, wherePoints of intersection are P and Q and PA and PB are their diameter respectively.Join PQ, AQ and QB.∴ ∠AQP = 90° and ∠BQP = 90°(Angle in a semicircle is a right angle)Adding both these angles,∠AQP + ∠BQP = 180°∠AQB = 180°

Let O and ' O be the centres of two intersecting circle, wherePoints of intersection are P and Q and PA and PB are their diameter respectively.Join PQ, AQ and QB.∴ ∠AQP = 90° and ∠BQP = 90°(Angle in a semicircle is a right angle)Adding both these angles,∠AQP + ∠BQP = 180°∠AQB = 180°Hence, the points A, Q and B are collinear.

Answer 2

Answer:

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