Find the area of a right angled triangle if the radius of its circumcircle is 3 cm and altitude drawn to the hypotenuse is 2 cm.

Solution

Let ABC be the right angled triangle right angled at B. Let O be the centre of the circumcircle.
Then, O is the mid-point of the hypotenuse
AC. | by geometry
OA = OB = OC
= radius of the circumcircle = 3 cm

∴ Hypotenuse AC = Diameter of the circle
= 2 x radius of the circumcircle
= 2 x 3 = 6
cm Let BM be the perpendicular from B on AC.
∴ BM = 2 cm
∴ Area of the right angled triangle ABC
$equals 1 half cross times space Base cross times Altitude equals 1 half cross times AC cross times BM equals 1 half cross times 6 cross times 2 equals 6 space cm squared$

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Statistics

Find the area of a right angled triangle if the radius of its circumcircle is 3 cm and altitude drawn to the hypotenuse is 2 cm.

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