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Area between Two Curves

Ntext ABC is ...

Question

\(\text {ABC is an isosceles triangle inscribed in a circle of radius r. If AB = AC and h is the altitude from A to BC, then the triangle has area A is equal to

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Solution

The correct option is B

\(In~ \Delta ABC, AB = BC \text{and altitude} AD = h\\
\text{Let r be the radius of circumscribed circle.}\\

$∴ P A = P B = P C = r$
$∴ P D = h - r$
Now, $B D = \sqrt{B P^{2} - P D^{2}}$
$= \sqrt{r^{2} - (h - r)^{2}}$
$= \sqrt{2 r h - h^{2}}$
$∴ B C = 2 B D = 2 \sqrt{2 r h - h^{2}}$
$Thus, are of Δ A B C = \frac{1}{2} \times B C \times D A$

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