Question

If circles are drawn taking two sides of a triangle as diameters , prove that the point of intersection of these circles lie on the third side ​

Answer 1

Answer:

Two circles are drawn on the sides AB and AC of the triangle

ABC as diameters. The circles intersected at D.

Construction: AD is joined.

To prove: D lies on BC. We have to prove that BDC is a straight line.

Proof:

∠ADB=∠ADC=90° ...Angle in the semi circle

Now,

∠ADB+∠ADC=180°

⇒∠BDC is straight line.

Thus, D lies on the BC.

Answer 2

Answer:

We know that an angle in a semicircle is a right angle. By using this fact, we can show that BDC is a line that will lead to proving that the point of intersection lies on the third side. ⇒ BDC is a straight line. Hence, the point of intersection of circles lies on the third side BC.

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I hope this helps