Question

if a circle is 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

Hello mate ☺

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Solution:

ABC is a triangle.

Taking side AC as diameter, we draw a circle and taking BC as diameter we draw another circle.

We need to prove that point D lies on the third side AB of ∆ABC.

AC is the diameter which means that ∠ADC=90°               .,......(1)(Angle in a semi-circle is equal to 90°)

Similarly, BC is the diameter which means that ∠BDC=90°     .........(2)(Angle in a semi-circle is equal to 90°)

From (1) and (2), we get ∠ADC+∠BDC=180° which means that ∠ADC and ∠BDC form a linear pair.

Therefore, points A, D and B are present on the same straight line.

I hope, this will help you.☺

Thank you______❤

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