List of top Quantitative Aptitude Questions on Geometry asked in CAT

Two circles of radii 6 cm and 6 cm intersect each other. The distance between their centers is 8 cm. What is the length of their common chord?

From an external point P, two tangents PA and PB are drawn to a circle with centre O. Radii OA and OB are perpendicular to the tangents and the angle \(\angle AOB = 50^\circ\). A third tangent is drawn which intersects both PA and PB. Find the angle \(\angle APB\).

In a triangle ABC, the sides are in the ratio 3 : 4 : 5. If the area of the triangle is 96 sq units, what is its perimeter?

A rectangle \(ABCD\) has sides \(AB = 45 \, \text{cm}\) and \(BC = 26 \, \text{cm}\). Point \(E\) is the midpoint of side \(CD\). Find the radius of the incircle of the triangle \(\triangle AED\).

A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is

A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC = 90°. If BC = 10 inches then the area of the triangle in square inches is

If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

The cost of fencing a rectangular plot is ₹ 200 per ft along one side, and ₹ 100 per ft along the three other sides. If the area of the rectangular plot is 60000 sq. ft, then the lowest possible cost of fencing all four sides, in INR, is

A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is

Let ABCD be a parallelogram. The lengths of the side AD and the diagonal AC are 10 cm and 20 cm, respectively. If the angle \(∠ADC \) is equal to 30° then the area of the parallelogram, in sq. cm, is

In a triangle \(ABC , ∠ BCA =50°\). D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, then \(∠ FDE\), in degrees, is equal to

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is

If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

Suppose the length of each side of a regular hexagon ABCDEF is 2 cm. It T is the mid point of CD, then the length of AT, in cm, is

A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ABC = 90°. If BC = 10 inches then the area of the triangle in square inches is

The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is [This Question was asked as TITA]

The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is

Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is

With rectangular axes of coordinates, the number of paths from (1,1) to (8,10) via (4,6), where each step from any point (x, y) is either to (x, y+1) or to (x+1, y), is

Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

A cube of side 4 cm is painted on all its faces. If it is sliced into 1 cm cubes, how many 1 cm cubes will have exactly one face painted?