For an equilateral triangle, the ratio of the in-radius and the outer- radius is

AC is a chord of circle whose centre is at O. If B is any point on the arc AC and ∠OCA=20⁰ , then the magnitude of ∠ABC is

The two vowels touch each other internally. Their radii are 2 cm and 3 cm. What will be the length of the largest chord of the bigger circle outside the inner circle?

If the circumradius of an equilateral triangle be 10 cm, then the measure of its in-radius is

The diameter of the circle with center O is AB. PQ is the chord that does not intersect AB. Join AP and BQ. If ∠BAP = ∠ABQ,  then what will be ABQP?

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:

The side of a trapezium pyramid with a square base is 24 cm. and its height is 5 cm. What will be the area of its oblique surface in cm²?

The area of the triangle whose vertices are given by the coordinates (1, 2), (-4, -3) and (4, 1) is: