You may also like

problem icon

So Big

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2

problem icon

Strange Rectangle 2

Find the exact values of some trig. ratios from this rectangle in which a cyclic quadrilateral cuts off four right angled triangles.

problem icon

30-60-90 Polypuzzle

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

Gold Again

Age 16 to 18 Challenge Level:

fig1
Consider the rhombus as illustrated where $x$ is an unknown length, $AP = AD = x$ , angle $DAP = 36$ degrees and $P$ is a point on the diagonal $AC$ such that $PB = 1$ unit.

Without using a calculator, computer or tables find the exact values of

1. $\cos36^{\circ}\cos72^{\circ}$
2. $\cos36^{\circ} - \cos72^{\circ}.$


fig2 3. Draw these two diagrams as accurately as you can and measure the lengths $a$ and $b$. What do you notice? Can you prove it? (In each diagram there are two right angled triangles). fig 3