Question

Using a ruler and compass only.
(i) Construct a $△ABC$ with the following data.
$AB=3.5cm,BC=6cm$ and $\angle ABC={120}^{\circ }$
(ii) In the same diagram, draw a circle with $BC$ as diameter. Find a point $P$ on the circumference of the circle which is equidistant from $AB$ and $BC$.
(iii) Measure $\angle BCP$.

Answer 1

Steps of Construction.
(i) Draw a line $BC=6cm$.
(ii) With the help of the point $B$, draw $\angle ABC={120}^{\circ }$
(iii) Taking radius $3.5cm$, cut $BA=3.5cm$
(iv) Join $A-C$.
(v) Draw ${\perp }^r$ bisector $MN$ of $BC$.
(vi) Draw a circle $O$ as centre and $OC$ as radius.
(vii) Draw angle bisector of $\angle ABC$ which intersects circle at $P$.
(viii) Join $B-P$ and $C-P$
(ix) Now, $\angle BCP={30}^{\circ }$.