Question

In ΔABC, BE ⊥ AC and CF ⊥ AB. BE and CF intersect at O. Show that

Answer 1

In ΔBOF and ΔCOE, we have:

(Vertically opposite angles)

(Given)

(Angle sum property)

Thus, ΔBOF and ΔCOE are equiangular. Hence, ΔBOF ||| ΔCOE.

By Area theorem, the areas of two similar triangles are proportional to the squares of the corresponding sides.