CAT (QA) PYQs

A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio $a: b$. If the radius of the circle is $r$, then the area of the triangle is

The sum of the perimeters of an equlateral triangle and a rectangle is $90 \mathrm{~cm}$ the area, $T$ , of the triangle and the area, $R$ , of the rectangle, both in sq cm, satisfy the relationship $R=T^{2}$. If the sides of the rectangle are in the ratio $1: 3$, then the length, in cm , of the longer side of the rectangle, is

From an interior point of an equilateral triangle, perpendiculars are drawn on all three sides. The sum of the lengths of the three perpendiculars is $s$. Then the area of triangle is