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if an isosceles triangle ABC in which AB=AC=6cm , is inscribed in a circle of radius 9 cm , find the area of triangle.

Posted by Prajkt Sonkusare 6 years, 10 months ago

CBSE > Class 10 > Mathematics

2 answers

Avinash Saigal 6 years, 10 months ago

Ans. Given : A isoscele triangle ABC in which AB = AC = 6cm is inscribed in circle with center O and radius 9 cm. let AM = x cm In Quadrilaterla OABC OB = OC = 9 cm and AB = AC = 6 cm. it means it is Kite and diagonals of kite are perpendicular to each other, So OA ⊥ BC In Right∆AMC, => AM2 + MC2=AC2 ........ [Pythagoras Theorem] => MC2 = 62 - x2 = 36-x2 ........... (1) in Right∆OMC, => OM2 + (MC)2 = OC2 => => (9-x)2 + 36-x2 = 81 => => 81 + x2 -18x + 36 - x2 = 81 => 18x = 36 => x = 2 AM = 2 cm Now, MC = 62-22 = 36-4 = 32 = 42 cm As OM is Perpendicular to Chord BC So M is midpoint of BC. SO BC = 2 * MC = 2×42 = 82 cm Area of ∆ABC = 12×BC×AM = 12×82×2 = 82cm2 thank you???

Alinarathore Alinarathore 6 years, 10 months ago

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