An equilateral triangle ABC is inscribed in a circle with centre O. D is a point on the minor are BC and ∠CBD=40⁰. Find the measure of ∠BCD.

O is the centre of this circle. Tangent drawn from a point P, touches the circle at Q. If PQ = 24 cm and OQ = 10 cm, then what is the value of OP? 

In what ratio is the segment joining (-1,-12) and (3,4) divided by the x-axis?

If the incentre of an equilateral triangle lies inside the triangle and its radius is 3 cm, then the side of the equilateral triangle is

It is given that ∆ABC ≅ ∆PQR, AB = 5 cm, ∠B = 40°, and ∠A = 80°. Which of the following options is true?

The sides BA and DE of a regular pentagon are produced to meet at F. What is the measure of ∠EFA?

In ∆ABC, ∠C=90⁰, Point P and Q are on the sides AC and BC, respectively, such that  AP:PC=BQ:QC=1:2.Then, $${AQ^2+BP^2}\over AB^2$$  is equal to:

If ABC is an equilateral triangle and P, Q, R respectively denote the middle points of AB, BC, CA then.