Question

Two poles of height a meters and b meters are p meters apart. Prove that the height of the point of intersection of the lines joining the top of each pole to the foot of the opposite pole is given by $\frac{ab}{a+b}$ meters.

Answer 1

Let AB and CD be two poles of heights a meters and b meters respectively such that the poles are p meters apart i.e. AC=p meters. Suppose the lines AD and BC meet at O such that OL = h meters.
Let CL = x and LA = y. Then, x+y=p.

In $△ABCand△LOC$, we have