From a point within an equilateral triangle, perpendiculars drawn to the three sides, are 6 cm, 7 cm and 8 cm respectively. the length of the side of the triangle is:

Radius of a circle is 5 cm. Length of chord AB in this circle is 6 cm. What is the distance of this chord from the centre of the circle?

In a circle with centre O, a diameter AB is produced to a point P lying outside the circle and PT is a tangent to the circle at the point C on it. If ∠BPT = 36°, then what is the measure of ∠BCP?

The perimeter of a semi-circle is 25.7 cm. What is its diameter (in cm)? (π = 3.14)

If the arcs of square length in two circles subtend angles of 60° and 75° at their centres, the ratio of their radii is 

△ABC ∼ △DEF. If the areas of △ABC and △DEF are 100 cm² and 81 cm², respectively and the altitude of △DEF is 6.3 cm, then the corresponding altitude of △ABC is:

Find the area of the triangle whose sides are 5 cm, 12 cm and 13 cm.

A prism with a right triangular base is 25 cm high. If the shorter sides of the triangle are in the ratio of 1 : 2 and the volume of the prism is 100 cm³ , what is the length of the longest side of the triangle?