CAT Triangles previous year questions

15 Triangles questions from CAT 2021–2025 (Quant), each with its answer and a step-by-step solution.

• Q21In a △ ABC , points D and E are on the sides BC and AC, respectively. BE and AD intersect at point T such that…CAT 2025 Slot 2 · Quant · Triangles
• Q1A triangle ABC is formed with AB = AC = 50 cm and BC = 80 cm. Then, the sum of the lengths, in cm, of all three…CAT 2025 Slot 3 · Quant · Triangles
• Q18In △ ABC , AB=AC=12 cm and D is a point on side BC such that AD=8 cm. If AD is extended to a point E such that ∠ ACB=∠…CAT 2025 Slot 3 · Quant · Triangles
• Q19ABCD is a rectangle with sides AB=56 cm and BC=45 cm, and E is the midpoint of side CD. Then, the length, in cm, of…CAT 2024 Slot 1 · Quant · Triangles
• Q5ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2…CAT 2024 Slot 2 · Quant · Triangles
• Q7The midpoints of sides AB, BC, and AC in △ ABC are M, N, and P, respectively. The medians drawn from A, B, and C…CAT 2024 Slot 3 · Quant · Triangles
• Q19In 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…CAT 2023 Slot 1 · Quant · Triangles
• Q17Let △ ABC be an isosceles triangle such that AB and AC are of equal length. AD is the altitude from A on BC and BE is…CAT 2023 Slot 3 · Quant · Triangles
• Q1In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If ∠ BAC=45^(∘) and ∠ ABC=θ , then…CAT 2022 Slot 2 · Quant · Triangles
• Q21The 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…CAT 2022 Slot 2 · Quant · Triangles
• Q7Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm., then,…CAT 2022 Slot 3 · Quant · Triangles
• Q21Two ships are approaching a port along straight routes at constant speeds. Initially, the two ships and the port…CAT 2022 Slot 3 · Quant · Triangles
• Q10A circle of diameter 8 inches is inscribed in a triangle ABC where ∠ ABC=90^(∘) . If BC=10 inches then the area of the…CAT 2021 Slot 1 · Quant · Triangles
• Q11Let 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 .…CAT 2021 Slot 2 · Quant · Triangles
• Q5In 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…CAT 2021 Slot 3 · Quant · Triangles