Question

Circles are described on the sides of a triangle as diameters. Prove that the circles on any two sides intersect each other on the third side (or third side produced).

Answer 1

Given : Circles are described on the sides of a triangle as diameters.

 

To prove : The circles on any two sides intersect each other on the third side (or third side produced).

Construction: Join AD

 

Proof :

Let two circles are drawn with sides AB and AC of the triangle ΔABC as diameters.  

 

Since,AC and AB are the diameters of the two circles.

∠ADB =90°............(i)

∠ADC = 90°..........(ii)

(Angle in the semi circle)

On adding eq i & ii

∠ADB + ∠ADC = 180°

∠BDC = 180°

Hence,BDC is a straight line.

So ,circles are drawn with sides AB and AC of the triangle ΔABC as diameters intersect at D , a point on BC (third side).

HOPE THIS ANSWER WILL HELP YOU…

 

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Answer 2

Answer:

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