Two circles are drawn with sides AB and AC of a triangle ABC as diameters. The circles intersect at a point D. If AB=5 cm, BD=3 cm , AC= 6 cm. Find BC

Dear student

Join AD.Since angle in a semi-circle is a right angle.Therefore, ADB=ADC=90°Now, In ADB by Pythagoras theroemAB2=AD2+BD252=AD2+32AD2=25-9AD=4cmIn ADC, by Pythagoras theoremAC2=AD2+DC262=42+DC2DC2=36-16DC=20DC=25So, BC=BD+DC=3+25cm

Regards

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