5√2 cm in a circle. If the long chord makes a right angle at the centre, then what will be the length of the radius of the circle?

If △ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.

Areas of two similar triangles are 36 cm² and 100 cm². If the length of a side of the larger triangle is 20 cm, then the length of the corresponding side of the similar triangle is:

In ΔPQR, PQ=QR and O is an interior point of ΔPQR such that ∠OPR=∠ORP.

Consider the following statements:

(i) ΔPOR is an isosceles triangle.

(ii) O is the centroid of ΔPQR.

(iii) ΔPQO is congruent to ΔRQO.

Which of the above statements are correct?

A cube has sides that are 4 cm each, and the dimensions of a cuboid are 2cm x 3cm x 4cm. Find the positive difference between the volume of the cube and that of the cuboid.

In △PQR, ∠P = 90°. S and T are the mid points of sides PR and PQ, respectively. What is the value of RQ²/(QS²+ RT²)?

AC is a chord of circle whose centre is at O. If B is any point on the arc AC and ∠OCA=20⁰ , then the magnitude of ∠ABC is

On increasing the radius of circle by 1 cm, its area is increased by 44 cm² .The original radius of the circle is -