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

The side QR of an equilateral triangle PQR is produced to the point S in such a way that QR = RS and P is joined to S. Then the measure of ∠PSR is

In a triangle, if orthocentre, circumcentre, incentre and centroid coincide, then the triangle must be

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

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

Let ABC be an equilateral triangle and AX, BY, CZ be the altitudes. Then the right statement out of the four given responses is

If in a triangle, the circumcenter, incentre, centroid and orthocenter coincide, then the triangle is

If the orthocenter and the centroid of a triangle are the same, then the triangle is: