In the diagram, $P$ is the midpoint of $CB$. The points $M$ and $N$ lie on $AB$ such that&

Question

In the diagram, $P$ is the midpoint of $CB$. The points $M$ and $N$ lie on $AB$ such that $AM=MN=NB$. Show that triangles $MCB$ and $NPB$ are similar. Find the fraction of the triangle which is shaded.

Accepted Answer

$\text{(i)}\ \triangle MCB\sim\triangle NPB\text{ (SAS)}$ $\text{(ii)}\ \dfrac{1}{6}$

Ratio and Proportion in Nested Triangles

Ratio and Proportion in Nested Triangles

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