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CBSE Class 9 Mathematics Question 18 of 20

Circles — Question 10

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Question 10

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

Two circles are drawn taking sides AB and AC as diameter.

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. NCERT Class 9 Mathematics CBSE Solutions.

⇒ ∠ADB = ∠ADC = 90° (Angles in the semi circle is a right angle.)

⇒ ∠ADB + ∠ADC = 90° + 90°

⇒ ∠ADB + ∠ADC = 180°

∴ BDC is straight line.

Thus, D lies on BC.

Hence, proved that the point of intersection of circles lie on the third side.