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

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

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

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

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?

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