Question

By constructing an equilateral triangle with side $4.5$ cm and its circumscribed circle, find the radius of the circumscribed circle

• A. $2$ cm
• B. $3.8$ cm
• C. $4.5$cm
• D. $3$ cm

Answer 1

The correct option is D $3$ cm

$△ABC$ is a equilateral triangle.

So, $AB=BC=AC=4.5$ cm

Now, draw perpendicular bisectors of sides $AB,BC$ and $AC$ by drawing arcs from each corner of the line.

$AD,BE,CF$ bisects the sides $BC,AC$ and $AB$ at $D,E$ and $F$ respectively.

Name the point of intersection of these bisectors as $P$ which becomes centroid of the triangle $ABC$.

Take $P$ as the centre and draw a circumscribed circle touching every vertices of $△ABC$.

As $P$ is the centroid of $△ABC$, $P$ divides each median in the ratio $2:1$.

Now, $\frac{4.5}{3}=1.5$

$⟹AP=2\times 1.5=3=BP=CP$ and $PD=1.5=PE=PF$

Now, $P$ is the centre of the circumscribed circle and $PD=PE=PF=1.5$ which forms radius of the circle.

Hence, radius of the circumscribed circle is $3$ cm.