Construct an isosceles triangle ABC such that AB=6 cm, BC=AC=4 cm.Bisect $∠ C$ internally and mark a point P on this bisector such that CP=5 cm.Find the points Q and R which are 5 cm from P and also 5 cm from the line AB.

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Solution

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Steps of Construction:

i) Draw a line segment AB = 6 cm.

ii) With centers A and B and radius 4 cm, draw two arcs which intersect each other at C.

iii) Join CA and CB.

iv) Draw the angle bisector of angle C and cut off CP = 5 cm.

v) A line m is drawn parallel to AB at a distance of 5 cm.

vi) P as centre and radius 5 cm, draw arcs which intersect the line m at Q and R.

vii) Join PQ, PR and AQ.

Q and R are the required points

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