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

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?

Each exterior angle of a regular polygon measures 9°. How many sides does the polygon have?

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)?

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 △ABC, M and N are the points on side BC such that AM ⊥ BC, AN is the bisector of ∠A, and M lies between B and N. If ∠B = 68°, and ∠C=26°, then the measure of ∠MAN is:

In an isosceles triangle, if the unequal angle is twice the sum of the equal angles, then each equal angle is

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.