An isosceles △ ABC is inscribed in a circle. If AB = AC = cm and BC = 24 cm, find the radius of the circle.

Question

KnowledgeBoat · Accepted Answer

Given, AB = AC = cm In an isosceles triangle, the perpendicular from a vertex between equal sides bisects the opposite side. Thus, L is the mid-point of BC. BL = = 12 cm. AL is perpendicular bisector of BC and perpendicular from center bisects the chord. Thus, centre of the circle O lies on AL. Let radius of circle OB be r. In right-angled triangle ALB, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ AB2 = AL2 + BL2 ⇒ ()2 = AL2 + 122 ⇒ 720 = AL2 + 144 ⇒ AL2 = 720 - 144 ⇒ AL2 = 576 ⇒ AL = = 24 cm OL = AL - AO = 24 - r In right-angled triangle OBL, By pythagoras theorem, ⇒ Hypotenuse2 = Perpendicular2 + Base2 ⇒ OB2 = OL2 + BL2 ⇒ r2 = (24 - r)2 + 122 ⇒ r2 = r2 - 48r + 576 + 144 ⇒ 48r = 720 ⇒ r = = 15 cm Hence, radius of the circle = 15 cm.

Mathematics

An isosceles △ ABC is inscribed in a circle. If AB = AC = cm and BC = 24 cm, find the radius of the circle.

Circles

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