Question

Construct a triangle XYZ in which XY=YZ=4.5 cm and ZX=5.4 cm.
Draw the circumcircle of the traingle and measure its circumradius.

Answer 1

Steps of construction :

$\left(i\right)$ Draw a line $XY=4.5cm$

$\left(ii\right)$ With the help of compass, draw an arc of $4.5cm$ from $Y$ as centre

$\left(iii\right)$ Again with the help of compass, draw another arc of $5.4cm$ from $A$ as centre which intersect the previous arc made by $Y$

$\left(iv\right)$ Now, marks the intersection as point $Z$ and join it to both $X$ and $Y$ the required triangle $XYZ$ is obtained

$\left(v\right)$ Draw the bisectors of $XY$ and $YZ$ which meet at point $O$

$\left(vi\right)$ Taking $O$ as centre and radius $OX$ or $OY$ or $OZ$ draw a circle using compass

$\left(vii\right)$ This circle will pass through the vertices $X,Y$ and $Z$