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

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:

In a triangle, if three altitudes are equal, then the triangle is 

The radii of two concentric circles are 17 cm and 25 cm. a straight line PQRS intersects the larger circle at the points P and S and intersects the smaller circle at the points Q and R. If QR = 16 cm, then the length (in cm.) of PS is 

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

AB is a chord of a circle in minor segment with center O.C is a point on the minorarc of the circle between the points A and B. The tangents to the circle at A and B meet at the point P. If ∠ACB = 102⁰ , then what is the measure of ∠APB?

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