TrianglesCAT Previous-Year Questions

5 previous-year questions on Triangles from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.

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5 questions

Triangles · CAT PYQs

CAT 2024 Slot 2 · QA
Q1.

The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is

CAT 2019 Slot 1 · QA
Q2.

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

CAT 2018 Slot 2 · QA
Q3.

A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0, 0) is

CAT 2005 · QA
Passage / Data

Answer the next 2 questions based on the information given below.

Ram and Shyam run a race between points A and B, 5 km apart. Ram starts at 9 a.m. from A at a speed of 5 km/hr, reaches B, and returns to A at the same speed. Shyam starts at 9:45 a.m. from A at  a speed of 10 km/hr, reaches B and comes back to A at the same speed.

Q4.

Consider a triangle drawn on the X-Y plane with its three vertices at (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

CAT 2002 · QA
Passage / Data

Sum of first n natural numbers = S(n)

Sum given by student = 575

S(10) = 10×112= 55

S(20) = 20×212= 210

S(30) = 30×312= 465

S(40) = 40×412= 820

∴ The student stopped counting somewhere between 30 and 40.

Consider S(35) = 36×352= 630

The student stopped somewhere before 35.

∴ S(31) = 496, S(32) = 528, S(33) = 561 and S(34) = 595

But the student gave 575 as the sum, so the student missed on the number 20.

Hence, option 4.

Q5.

The area of the triangle with the vertices (a, a), (a + 1, a) and (a, a + 2) is