You may also like

problem icon

Incircles Explained

This article is about triangles in which the lengths of the sides and the radii of the inscribed circles are all whole numbers.

problem icon

Xtra

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations.

problem icon

Impossible Triangles?

Which of these triangular jigsaws are impossible to finish?

Area I'n It

Age 16 to 18 Challenge Level:

Triangle $ABC$ has altitudes $h_1$, $h_2$ and $h_3$.

The radius of the inscribed circle is $r$, while the radii of the escribed circles are $r_1$, $r_2$ and $r_3$ respectively.

Prove:

$\begin{equation} \frac{1}{r} = \frac{1}{h_1} + \frac{1}{h_2} + \frac{1}{h_3} = \frac{1}{r_1} + \frac{1}{r_2} + \frac{1}{r_3}. \end{equation}$

Area