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# Check below? (geometry involved)

## Question

###### Check below? (geometry involved)

Given isosceles triangle $A \hat{B} C$ $\left(A B = A C\right)$ circumscribed in a circle with radius $r = 1$ .

Consider $x$ the height of the triangle $A \hat{B} C$ from the vertex $A$.

• a) Prove that $B C = 2 \sqrt{\frac{x}{x - 2}}$ $\textcolor{w h i t e}{a a}$ , $x > 2$

• b) Find the value of $x$ for which the area of the triangle $A \hat{B} C$ is minimum

• c) The side $B C$ of the triangle is changing with a rate of $\sqrt{3}$ $\frac{c m}{\sec}$. Find the rate of change for the angle $\hat{A}$ when the triangle becomes equilateral

(Area is given as a function of $x$)

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