List of top Quantitative Aptitude Questions on Triangles, Circles & Quadrilaterals asked in CAT

A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is

Let \(ΔABC\) be an isosceles triangle such that \(AB\) and \(AC\) are of equal length. \(AD\) is the altitude from \(A\) on \(BC\) and \(BE\) is the altitude from \(B\) on \(AC\) . If \(AD\) and \(BE\) intersect at \(O\) such that \(∠AOB =105\degree\) , then \(\frac{AD}{BE}\) equals

Let \(C_1\) and \(C_2\) be concentric circles such that the diameter of \(C_1\) is 2 cm longer than that of \(C_2\). If a chord of \(C_1\) has length 6 cm and is a tangent to \(C_2\), then the diameter, in cm, of \(C_1\) is
[This Question was asked as TITA]

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 the triangle is

Let \(C_1\) and \(C_2\) be concentric circles such that the diameter of \(C_1\) is \(2\) cm longer than that of \(C_2\). If a chord of \(C_1\) has length \(6\) cm and is a tangent to \(C_2\), then the diameter, in cm, of \(C_1\) is

Let C be a circle of radius 5 meters having center at O. Let PQ be a chord of C that passes through points A and B where A is located 4 meters north of O and B is located 3 meters east of O. Then, the length of PQ, in meters, is nearest to

Two circular tracks T1 and T2 of radii 100 m and 20 m, respectively touch at a point A. Starting from A at the same time, Ram and Rahim are walking on track T1 and track T2 at speeds 15 km/hr and 5 km/hr respectively. The number of full rounds that Ram will make before he meets Rahim again for the first time is

The sum of the perimeters of an equilateral triangle and a rectangle is 90 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