A circle is inscribed in a equilateral triangle of side 24 cm. What is the area ( in cm²) of a square inscribed in the circle?

ABC is an isosceles triangle with AB = AC. The side BA is produced to D such that AB = AD. If ∠ABC = 30°, then ∠BCD is equal to 

In an isosceles triangles ABC, AB=AC the median drawn on the same arms are perpendicular to each other find AB/BC?

The largest and the second largest angles of a triangle are in the ratio of 3 : 2 respectively. The smallest angle is 20% of the sum of the rest two angles. What is the sum of the smallest and the second largest angles?

Two circles having radii 5 units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is

The maximum number of common tangents drawn to two circles when both the circles touch each other externally 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?

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?