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

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:

If ABC is an equilateral triangle and D is a point on BC such that AD⊥BC, then 

AB is a diameter of a circle with centre O. The tangents at C meets AB produced at Q. If ∠CAB = 34°, then measure of ∠CBA is

In ∆PQR, O is the incentre and ∠P = 42°. Then what is the measure of ∠QOR?

If C₁, C₂ be the centres of rwo circles and r₁, r₂ be the respective radii such that the distance between the centres is equal to the sum of the radii of the two circles, find the number of common tangents.