Using ruler and compasses only, construct a $\triangle ABC$, from the following data:
$AB + BC + CA = 12\ cm, \angle B = 45^o$ and $\angle C = 60^o$.
Given:
$AB + BC + CA = 12\ cm, \angle B = 45^o$ and $\angle C = 60^o$.
To do:
We have to construct the given triangle.
Solution:
Steps of construction:
(i) Draw a line segment $PQ = 12\ cm$.
(ii) Draw ray $PX$ at $P$ making an angle of $45^o$ and at $Q, QY$ making an angle of $60^o$.
(iii) Draw the angle bisectors of $\angle P$ and $\angle Q$ meeting each other at $A$.
(iv) Draw the perpendicular bisector of $AP$ and $AQ$ intersecting $PQ$ at $B$ and $C$ respectively.
(v) Join $AB$ and $AC$.
Therefore,
$\triangle ABC$ is the required triangle.
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