Question
Draw a triangle $ABC$ with $AB = 3\ cm, BC = 4\ cm$ and $\angle\text{B}=60^\circ.$ Also, draw the bisector of angles $C$ and $A$ of the triangle, meeting in a point $O$. Measure $\angle\text{COA}.$
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Answer
Steps of construction: Step I: Draw a line segment $B C=4 cm$.
Step II: Draw $\angle CBX =60^{\circ}$.
Step III: Draw an arc on $BX$ at a radius of $3 cm$ cutting $B X$ at $A$.
Step IV: Join $AC$ to get the required triangle.
Angle bisector for angle A:
Step I: With $A$ as centre, cut arcs of the same radius cutting $A B$ and $A C$ at $P$ and $Q$, respectively.
Step II: From $P$ and $Q$ cut arcs of same radius intersecting at $R$.
Step II: Join AR to get the angle bisector of angle$ A.$
Angle bisector for angle C:
Step I: With A as centre, cut arcs of the same radius cutting $CB$ and $CA$ at $M$ and $N$, respectively.
Step II: From $M$ and $N$, cut arcs of the same radius intersecting at $T$
Step III: Join $CT$ to get the angle bisector of angle $C.$
Step IV: Mark the point of intersection of $CT$ and $AR$ as $0 .$
Step V: Angle $\angle COA =120^{\circ}$.
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