CAT QA LINES ANGLES TRIANGLES QUESTIONS

The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of △ ABC is 1440 sq cm, then the area, in sq cm, of △ XYZ is

In a right-angled triangle ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, is

Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm., then, the area of the triangle EOD, in sq. cm., is

The length of each side of an equilateral triangle ABC is 3 cm. Let D be a point on BC such that the area of triangle ADC is half the area of triangle ABD. Then the length of AD, in 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

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

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

In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respectively. Then, the area of triangle ABC, in sq cm, is

Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is.

Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will be

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4(√2 - 1) cm, then the area, in sq. cm, of the triangle ABC is

From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is:

Let ABC be a right-angled isosceles triangle with hypotenuse BC. Let BQC be a semi-circle, away from A, with diameter BC. Let BPC be an arc of a circle centered at A and lying between BC and BQC. If AB has length 6 cm then the area, in sq. cm, of the region enclosed by BPC and BQC is:

Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is: 

If altitude of a triangle is 30,50 and 3n, then how many possible values of “n” (where n is a natural number).

In the given figure, ABC is a right-angle triangle and BDEF is the maximum sized square inside triangle. Area of the triangle AFE and EDC are 27 units and 48units respectively. Find the area of the triangle?

In right angle triangle PQR has PR = 10, PQ = 26, and QR = 24. The perpendicular bisector of RT intersects the extension of RP at O. Find OQ.

In the given figure, find the length of AD in cm.

Let ABC be a right-angled triangle with circumradius R = 15 and inradius r = 6. Find the area of the triangle ABC.

In a ∆ABC, AD & BE are medians and G is the centroid, ∠AGE = 30° , AD=9cm & BE= 12 cm, Find the area of the triangle?

Existence of a triangle is possible if

Find the area of the maximum sized square (PQRS) inside a right-angle triangle ABC and one side of the square lies on the hypotenuse such that AB=3 cm, AC=4 cm and BC=5cm.

What is the distance between Centre of circumcircle and in circle drawn to 12-16-20 triangle.

Roxx has a triangle with area 9√3. What’s the smallest perimeter it could have?