Mathematics
Two circles intersect at P and Q. Through P diameters PA and PB of the two circles are drawn. Show that the points A, Q and B are collinear.
Circles
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Answer
Let O and O' be the centres of two intersecting circles, where points of the intersection are P and Q and PA and PB are their diameters respectively.
As angle in a semicircle is a right angle.
∴ ∠AQP = 90° and ∠BQP = 90°
Adding,
⇒ ∠AQP + ∠BQP = 180°
⇒ ∠AQB = 180°.
Hence, the points A, Q and B are collinear.
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