In the given figure, PQR is an equilateral triangle with side as 12 cm. S and T are the midpoints of the sides PQ and PR respectively. What is the area (in cm²) of the shaded region?

Ratio of the number of sides of two regular polygons is 5 : 6 and the ratio of their each interior angle is 24 : 25. Then the number of sides of these two polygons are 

Given that DE || BC, AD : DB = 3 : 4, find out ar(∆ADE)/ar(∆ABC)?

∠A, ∠B, ∠C are three angles of a triangle. If ∠A -∠B =18°, ∠B – ∠C = 45°, then, ∠B, ∠A and ∠C are

A unique circle can always be drawn through x number of given non-collinear points, then X must be 

ABCD is cyclic quadrilateral Sides AB and DC, when produced, meet at E, and sides BC and AD, When produced, meet at F. If ∠BFA=60° and ∠AED=30°, then the measure of ∠ABC is:

In the triangle ABC, AB = 2 cm, BC = 3 cm and AC = 4 cm. D is the middle point of AC. If a square is constructed on the side BC, what is the area of the square?

ΔABC is an equilateral triangle in which D, E and F are the points on sides BC, AC and AB, respectively, such that AD ⊥ BC, BE ⊥ AC and CF ⊥ AB. Which of the following is true?