Question
Draw a $\triangle\text{ABC}$ with $AB = 6cm, BC = 7cm$ and $CA = 8cm.$ Using ruler and compass alone, draw $(i)$ the bisector $AD$ of $\angle\text{A}$ and $(ii)$ perpendicular $AL$ from A on $BC$. Measure $LAD.$
✓
Answer
Steps of construction: Step I: Draw a line segment $BC$ of length $7 cm .$
Step II: With centre $B$, draw an arc of radius $6 cm$ .
Step III: With centre $C$, draw an arc of radius $8 cm$ intersecting the previously drawn arc at $A.$
Step IV: Join $A C$ and $B C$ to get the required triangle.
Angle bisector steps: Step I: From $A$, cut arcs of equal radius intersecting $A B$ and $A C$ at $E$ and $F$ respectively.
Step II: From $E$ and $F,$ cut arcs of equal radius intersecting at point $H.$
Step III: Join $AH$ and extend to produce the angle bisector of angle $A$, meeting line $B C$ at $D$.
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