Question

In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point in side AC such that AP = 6 cm. Prove that $\Delta BPC$ is similar to $\Delta ABC$. Also, find the length of BP.

• A. BP = 4 cm
• B. BP = 8 cm
• C. BP = 6 cm
• D. BP = 12 cm

Answer 1

The correct option is A BP = 4 cm

Given: $△ABC$, $AB=AC=8$, $BC=4$ and $AP=6$
In $\Delta ABC$,
$\frac{AB}{BC}=\frac{8}{4}=2$,
In $\Delta BPC$,
$\frac{BC}{CP}=\frac{4}{2}=2$
Now, in $△ABC$ and $△BPC$
$\frac{AB}{BC}=\frac{BC}{CP}$
$\angle ABC=\angle C.$
Therefore, by SAS, $\Delta ABC\sim \Delta BPC$
Thus, $\frac{AB}{BP}=\frac{AC}{BC}$

$\frac{8}{BP}=\frac{8}{4}$
$BP=4$ cm