IPMAT Geometry Questions 2026 With Video Solutions

The number of triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line is_________.

In triangle ABC, AB = AC = x, $$\angle ABC = \theta$$ and the circumradius is equal to y. Then $$\dfrac{x}{y}$$ equals

A circle touches the y-axis at (0, 4) and passes through the point (-2, 0). Then, the radius of the circle is

On a circular path of radius 6 m a boy starts from a point A on the circumference and walks along a chord AB of length 3 m. He then walks along another chord BC of length 2 m to reach point C. The point B lies on the minor arc AC. The distance between point C from point A is

Let $$\triangle ABC$$ be a triangle with $$AB = AC$$ and $$D$$ be a point on $$BC$$ such that $$\angle BAD = 30^\circ$$. If E is a point on $$AC$$ such that $$AD = AE$$, then $$\angle CDE$$ equals

Let $$\triangle ABC$$ be a triangle right-angled at B with AB = BC = 18. The area of the largest rectangle that can be inscribed in this triangle and has B as one of the vertices is:

Let ABC be an equilateral triangle, with each side of length k. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is

Points P, Q, R and S are taken on sides AB, BC, CD and DA of square ABCD respectively, so that AP : PB = BQ : QC = CR : RD = DS : SA = 1 : n . Then the ratio of the area of PQRS to the area of ABCD is

In a triangle ABC, let D be the mid-point of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be

ABCD is a quadrilateral whose diagonals AC and BD intersect at O. If triangles AOB and COD have areas 4 and 9 respectively, then the minimum area that ABCD can have is

The sum of the interior angles of a convex n-sided polygon is less than $$2019^{\circ}$$. The maximum possible value of n is

A circle of radius 13 cm touches the adjacent sides AB and BC of a square ABCD at M and N, respectively. If AB = 18 cm and the circle intersects the other two sides CD and DA at P and Q, respectively, then the area, in sq. cm, of triangle PMD is

A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, two circles are drawn, one on each side of the chord, each touching the chord at its midpoint and the original circle. Let k be the ratio of the areas of the bigger inscribed circle and the smaller inscribed circle, then k equals

If the angles A, B,C of a triangle are in arithmetic progression such that $$\sin(2A + B) = 1/2$$ then $$\sin(B + 2C)$$ is equal to

The lengths of the sides of a triangle are x, 21 and 40, where x is the shortest side. A possible value of x is

The number of acute angled triangles whose sides are three consecutive positive integers and whose perimeter is at most 100 is

Area of a regular octagon inscribed in a circle of radius 1 unit is:

If the shortest distance of a given point to a given circle is 4 cm and the longest distance is 9 cm, then the radius of the circle is

In a right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of sides AB and AC is found to be 6 cm in length. The length of BC is

Consider a triangle with side lengths 4 meters, 6 meters, and 9 meters. A dog runs around the triangle in such a way that the shortest distance of the dog from the triangle is exactly 1 meter. The total distance covered (in meters) by the dog in one round is

The number of triangles with integer sides and with perimeter 15 is: