Triangle and its various kinds of centres

If the areas of two similar triangles are in the ratio $121 : 225$, what would be the ratio of the corresponding sides?...

ΔABC is inscribed in a circle with centre O. If the sides of the triangle are $AB = 21 \text{ cm}$, $BC = 20 \text{ cm}$...

**In ΔPQR, PQ = QR and O is an interior point of ΔPQR such that ∠OPR = ∠ORP. Consider the following statements:** (i) Δ...

A circle touches all four sides of a quadrilateral ABCD. If $AB = 18 \text{ cm}$, $BC = 21 \text{ cm}$ and $AD = 15 \tex...

From the top of an upright pole $17.75 \text{ m}$ high, the angle of elevation of the top of an upright tower was $60^\c...

If the areas of two similar triangles are in the ratio $196 : 625$, what is the ratio of their corresponding sides?...

The breadth \( b \) of a room is twice its height and half of its length. Find the length of the longest diagonal of the...

If the exterior angle of a regular polygon is $18^\circ$, then find the number of diagonals in this polygon....

ABCD is a cyclic quadrilateral and BC is a diameter of the circle on which points A and D also lie. Given that $\angle B...

The centroid of an equilateral triangle PQR is L. If $PQ = 6 \text{ cm}$, what is the length of $PL$?...

Find the number of diagonals of a regular polygon, the sum of whose interior angles is $2700^\circ$....

What is the perimeter of a square inscribed in a circle of radius $5 \text{ cm}$?...

It is given that $\triangle ABC \cong \triangle PQR$, $AB = 5 \text{ cm}$, $\angle B = 40^\circ$, and $\angle A = 80^\ci...

PQRS is a cyclic quadrilateral. If \(\angle P\) is three times \(\angle R\) and \(\angle S\) is four times \(\angle Q\),...

If one of the interior angles of a regular polygon is $\frac{15}{16}$ times one of the interior angles of a regular deca...

In a trapezium ABCD, AB and DC are parallel with a perpendicular distance of $8 \text{ m}$ between them. The non-paralle...

An equilateral triangle ABC surmounts a square BCDE such that side BC is common to both. Given this configuration, find ...

In a circle with centre $O$, an arc $ABC$ subtends an angle of $134^ ext{o}$ at the centre of the circle. The chord $AB$...

In a circle centered at $O$, a diameter $AB$ is extended to a point $C$ outside the circle. $CD$ is a tangent at point $...

In a circle centered at $O$, a diameter $AB$ is extended to a point $C$ outside the circle. If $CD = 7\sqrt{3} \text{ cm...

ABCD is a quadrilateral with diagonal $BD = 70 \text{ cm}$. Perpendiculars from vertices $A$ and $C$ to diagonal $BD$ ar...