CAT 2017 Geometry & Mensuration Question (Hard)

Question

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4 2 - 1 cm, then the area, in sq. cm, of the triangle ABC is TITA

Accepted Answer

Step 1 Let the side length of the right-angled isosceles triangle be . Since it is right-angled and isosceles, the legs and are equal, and is the hypotenuse. Area of triangle 1 2 x x x 2 Step 2 Let be any interior point. From geometry, the sum of perpendicular distances from an interior point to the

CAT 2017

Quantitative

Geometry & Mensuration

Hard

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4(√2 - 1) cm, then the area, in sq. cm, of the triangle ABC is [TITA

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