Using ruler and compasses only, construct an ΔABC, given base BC = 7 cm, ABC = 60° and AB+AC=12 cm.


We are asked to construct a triangle ABC in which BC = 7 cm, B = 60° and


AB + AC = 12 cm



We will follow the following algorithm for the construction


Steps of construction


STEP1: Draw BC of length 7 cm.


STEP2: With B as a centre, and convenient radius draw an arc cutting BC at N.


STEP3: With N as a centre, and same radius draw an arc cutting the previous arc at M.


STEP4: Draw BM and produce it to P.


STEP5: From BP, cut BR = 12 cm.


STEP6: Draw segment RC.


STEP7: Draw perpendicular bisector of RC. It cuts the ray BR at A.


STEP8: Draw AC.


ABC is the required triangle.


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