Question

$a$ and $b$ are real numbers between $0$ and $1.$ $A\equiv (a,1),B\equiv (1,b)$ and $C\equiv (0,0)$ are the vertices of a $△ABC$.

If the $△ABC$ is isosceles with $AC=BC$ and $5(AB{)}^2=2(AC{)}^2,$ then

• A. $a=\frac{1}{2}=b$
• B. $a=\frac{1}{4}$
• C. $b=1$
• D. $b=\frac{1}{4}$

Answer 1

The correct option is A $a=\frac{1}{2}=b$

$a^2+1=b^2+1$

Since

$AC=BC\Rightarrow a=b5\left(2{(a-1)}^2\right)=2(a^2+1)\Rightarrow a=b=\frac{1}{2}$