Content Writer | MBA Professional | Updated on - Nov 26, 2025
The CAT QA section requires speed and accuracy, along with a thorough understanding of the Triangles. This article provides a set of MCQs on Triangles to help you understand the topic and improve your problem-solving skills with the help of detailed solutions by ensuring conceptual clarity, which will help you in the CAT 2025 exam preparation
Whether you're revising the basics or testing your knowledge, these MCQs will serve as a valuable practice resource.
The CAT 2025 exam is expected to follow a similar trend to the CAT 2024, with 22 questions from the QA section out of a total of 68 questions.
1. ∆ABC is inscribed inside a circle and there is a point D on the arc BC opposite to A such that BD = CD. If ∠BAC = 70° and ∠ABD = 85°, then find the measure of ∠BCA.
2. In a ∆PQR, internal angle bisectors of ∠Q and ∠R meet at I while external angle bisectors of ∠Q and ∠R meet at X. If ∠P = 54°, then find the measures of ∠QIR and ∠QXR, respectively.
3. Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is
4. Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A,B, C, D, E, F, G, H, J, K, and O so as to form a triangle?
5. On a plate in the shape of an equilateral triangle \(ABC\) with area \(16\sqrt{3}\) sq cm, a rod \(GD\), of height 8 cm, is fixed vertically at the centre of the triangle. \(G\) is a point on the plate. If the areas of the triangles \(AGD\) and \(BGD\) are both equal to \(4\sqrt{19}\) sq cm, find the area of the triangle \(CGD\) (in sq cm).
6. In the figure, \(\triangle ABC\) is equilateral with area \(S\). \(M\) is the mid-point of \(BC\), and \(P\) is a point on \(AM\) extended such that \(MP = BM\). If the semi-circle on \(AP\) intersects \(CB\) extended at \(Q\), and the area of a square with \(MQ\) as a side is \(T\), which of the following is true?
∆ABC is inscribed inside a circle and there is a point D on the arc BC opposite to A such that BD = CD. If ∠BAC = 70° and ∠ABD = 85°, then find the measure of ∠BCA.
On a plate in the shape of an equilateral triangle \(ABC\) with area \(16\sqrt{3}\) sq cm, a rod \(GD\), of height 8 cm, is fixed vertically at the centre of the triangle. \(G\) is a point on the plate. If the areas of the triangles \(AGD\) and \(BGD\) are both equal to \(4\sqrt{19}\) sq cm, find the area of the triangle \(CGD\) (in sq cm).
Let AB, CD, EF, GH, and JK be five diameters of a circle with center at O. In how many ways can three points be chosen out of A,B, C, D, E, F, G, H, J, K, and O so as to form a triangle?
Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 krn, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is
What is the area of the triangle bounded by the graph of the function given by \(f(x) = |x - 1| - x\) with the coordinate axes given by \(x = 0\) and \(y = 0\)?
In the figure, \(\triangle ABC\) is equilateral with area \(S\). \(M\) is the mid-point of \(BC\), and \(P\) is a point on \(AM\) extended such that \(MP = BM\). If the semi-circle on \(AP\) intersects \(CB\) extended at \(Q\), and the area of a square with \(MQ\) as a side is \(T\), which of the following is true?
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