Construct a triangle ABC such that BC = 6 cm, AB = 6 cm and median AD = 4 cm.

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Solution

We are given and median

We have to construct the triangle ABC

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw a line segment BC of length 6 cm.

STEP2: Draw the perpendicular bisector of line BC cutting the line at point D, such that BD = 3 cm.

STEP3: With centre B and radius = 6 cm, draw an arc.

STEP4: With centre D and radius = 4 cm, draw an arc intersecting the previous arc at A.

STEP5: Draw AC to get the desired ΔABC.

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