Sine rule and cosine rule

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.

Explore the geometry of these dart and kite shapes!

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.

A white cross is placed symmetrically in a red disc with the central square of side length sqrt 2 and the arms of the cross of length 1 unit. What is the area of the disc still showing?

How far should the roof overhang to shade windows from the mid-day sun?

Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?

Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.