Question

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.

Answer 1

Steps of construction:
(i) Draw AB = 6 cm and cut arc of 4 cm from A and B these arcs intersect at C join AC and BC.
(ii) Draw the bisector (internal) of ∠ C and mark the point P, taking CP = 5 cm
(iii) Draw a line EF parallel to AB at a distance of 5 cm.
(iv) Take P as centre cut two points on line EF as PQ and PR are each equal to 5 cm.