Question

A line cuts two sides AB and AC of triangleABC at point P and Q respectively. Prove Area of triangleAPQ/area of triangleABC =APmultiplyAQ/AB multiply AC

Answer 1

Let ∠A = θ.

By the formula of the area of triangle,

$\triangle ABC=\frac{1}{2} \times AB \times AC \times sin \theta$,

$\triangle APQ=\frac{1}{2} \times AP \times AQ \times sin\theta$.

∴ $\frac{\triangle APQ}{\triangle ABC} =\frac{\frac{1}{2} \times AP \times AQ \times sin\theta}{\frac{1}{2} \times AB \times AC \times sin \theta} =\frac{AP \times AQ}{AB \times AC}$