Question

The radius of the circumcircle of $△ABC$ is:

• A. $6.3cm$
• B. $8cm$
• C. $7.2cm$
• D. $5.1cm$

Answer 1

The correct option is D $5.1cm$

• Draw a line segment $BC=7.2cm$. Construct $\angle CBD={45}^o$
• At $B$ on $BD$, construct a perpendicular.
• Now, draw perpendicular bisector of $BC$, which intersects the perpendicular of $BD$
• Taking $O$ as center and $OB$ as radius, draw a circle
• This circlepasses through $B$ and $C$. $BD$ is tangent
• $M$ as center, draw an arc of $8cm$ on circle. Arc cuts the circle at $A$
• Join $A,C$ and $A,B$
• $ABC$ is required triangle

Radius of circumcircle $2R=\frac{a}{\sin A}$

$a=7.2\angle A={45}^{o}R=\frac{a}{2\sin A}=\frac{7.2}{2\times \sin {45}^o}=\frac{7.2}{\sqrt{2}}=5.1cm$