Question

If $(\cos \alpha ,\sin \alpha ,0),(\cos ,\beta ,\sin \beta ,0),(\cos \gamma ,\sin \gamma ,0)$ are vertices of a triangle then circum radius $R$ is

• A. $1$
• B. $3$
• C. $2$
• D. $4$

Answer 1

The correct option is A $1$

$\text{Given,}$

$\text{the vertices of a}△ABC$

$A$=$(\cos \alpha ,\sin \alpha ,O)$

$B$=$(\cos \beta ,\sin \beta ,0)$

$C$=$(\cos y,\sin y,0)$

$\text{We know,}{\cos }^2\alpha +{\sin }^2\alpha =1$

similary, ${\cos }^2\beta +{\sin }^2\beta =1$

${\cos }^{2}y+{\sin }^{2}y=1$

Given, the circumradius $R$,

then, the equation of circumcircle

$x^2+y^2=R^2-\left(i\right)$

Putting $A$ on equation (1)

${\cos }^2\alpha +{\sin }^2\alpha =R^2$

$\Rightarrow R=1$

$\text{Cirumradius}R=1$