Question 68

ΔABC is a right angled triangle, the radius of its circumcircle is 3 cm and the length of its altitude drawn from the opposite vertex to the hypotenuse is 2 cm. Then the area of the triangle is

Solution

$$\triangle$$ ABC is right angled at B and BD is perpendicular to AC and BD = 2 cm

Circumcentre of a right angled triangle lies at the mid point of its hypotenuse

=> AD = CD

Thus, AC = $$2 \times $$ CD = 6 cm

$$\therefore$$ Area of $$\triangle$$ ABC = $$\frac{1}{2} \times BD \times CD$$

= $$\frac{1}{2} \times 2 \times 6=6$$ $$cm^2$$

=> Ans - (C)

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