Using ruler and compasses only, construct a $∆ABC$, given base $BC = 7\ cm, \angle ABC = 60^o$ and $AB + AC = 12\ cm$.
Given:
A $∆ABC$ in which $BC = 7\ cm, \angle ABC = 60^o$ and $AB + AC = 12\ cm$.
To do:
We have to construct the given triangle.
Solution:
Steps of construction:
(i) Draw a line segment $BC = 7\ cm$.
(ii) At $B$, draw a ray $BX$ making an angle of $60^o$ and cut off $BE = 12\ cm$.
(iii) Join $EC$.
(iv) Draw the perpendicular bisector of $EC$ which intersects $BE$ at $A$.
(v) Join $AC$.
Therefore,
$\triangle ABC$ is the required triangle.
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