Question

STATEMENT 1: The angle between equal sides of an isosceles triangle is ${60}^o$, then $r:R=1:2$.

STATEMENT 2: Every isosceles triangle is equilateral triangle.

• A. Statement-1 is true, Statement-2 is true, Statement-2 is correct explanation of Statement- 1.
• B. Statement-1 is true, Statement-2 is true, Statement-2 is not correct explanation for Statement-1.
• C. Statement-1 is true, Statement-2 is false.
• D. Statement-1 is false, Statement-2 is true.

Answer 1

The correct option is C Statement-1 is true, Statement-2 is false.

$R=\frac{a^3}{4\Delta }$

Also $r=\frac{\Delta }{s}$ and ${\Delta }_{eq}=\frac{a^2\sqrt{3}}{4}$

Thus $\frac{R}{r}=\frac{a^3\times s}{4\times {\Delta }^2}$

$=\frac{a^3\times 3a}{2\times 4\times \frac{a^4\times 3}{16}}$
$=2$

Hence $r:R=1:2$

Thus the statement $1$ is correct

The reason is not correct as for an isosceles triangle only two sides are equal while for an equilateral triangle all the three sides, are equal.

Thus the statement $2$ is incorrect