GEOMETRY 

In a square PQRS, A is any point such that AP:AQ:AC = 1:2:3 . Find ∠PAQ in degrees

In △ABC, ∠A: ∠B: ∠C = 1:2:4 .Prove that 1/AB + 1/AC = 1/BC 

Two circles of radii 2 and 3 cm touch each other externally . The length of direct common tangent to the two circles will be ?

Two adjacent vertices of a square are on a circle of radius R and the other two vertices lie on a tangent to the circle . The length of the side of the square is " xR" Find x 

Quadrilateral ABCD is inscribed inside a circle with ∠ BAC = 70° , ∠ADB = 40° , AD = 4 , and BC = 6 , What is (AC)²?

Points P and Q are on a circle of radius 5 and AB = 6 . Point R is the midpoint of the minor arc PQ . What is the length of the line segment PQ² ?