Triangles — CAT 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.
Triangles · CAT PYQs
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
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
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
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.
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
Sum of first n natural numbers = S(n)
Sum given by student = 575
S(10) = 55
S(20) = 210
S(30) = 465
S(40) = 820
∴ The student stopped counting somewhere between 30 and 40.
Consider S(35) = 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.
The area of the triangle with the vertices (a, a), (a + 1, a) and (a, a + 2) is