ABCD 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 radius of incircle of $\triangle ADE$ is
Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is
ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of $\triangle AEB$ is
A circular plot of land is divided into two regions by a chord of length $10\sqrt{3}$ meters such that the chord subtends an angle of 120° at the center. Then, the area, in square meters, of the smaller region is
A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is
The midpoints of sides AB, BC, and AC in ΔABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ΔABC is 1440 sq cm, then the area, in sq cm, of $\triangle XYZ$ is
Let △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 the altitude from B on AC. If AD and BE intersect at O such that $\angle \mathrm{AOB}=105^{\circ}\angle \mathrm{AOB}=105^{\circ}$, then $\frac{A D}{B E}$ equals
In a circle with centre $C$ and radius $6\sqrt{2}$ cm, $PQ$ and $SR$ are two parallel chords perpendicular to one of the diameters. $\angle PQC = 45^{\circ}$, and the ratio of the perpendicular distances of $PQ$ and $SR$ from $C$ is $3:2$. Then, the area, in sq. cm, of the quadrilateral $PQRS$ is:
If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is:
In a $\Delta ABC$, points D and E are on the sides BC and AC, respectively. BE and AD intersect at point T such that $AD: AT=4:3,$ and $BE: BT=5:4$. Point F lies on AC such that DF is parallel to BE. Then, $BD: CD$ is
Let ABCDEF be a regular hexagon and P and Q be the midpoints of AB and CD, respectively. Then, the ratio of the areas of trapezium PBCQ and hexagon ABCDEF is
Two tangents drawn from a point P touch a circle with center O at points Q and R. Points A and B lie on PQ and PR, respectively, such that AB is also a tangent to the same circle. If $\angle AOB = 50^\circ$, then $\angle APB$, in degrees, equals
ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and $AB=3DC$. If a circle inscribed in the trapezium touching all the sides has a radius of 3 cm, then the area, in sq. cm, of the trapezium is
In $\Delta ABC$, $AB=AC=12$ cm and D is a point on side BC such that $AD=8$ cm. If AD is extended to a point E such that $\angle ACB=\angle AEB$ then the length, in cm, of AE is
A triangle ABC is formed with $AB=AC=50$ cm and $BC=80$ cm. Then, the sum of the lengths, in cm, of all three altitudes of the triangle ABC is
