### 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.

### 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:

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