Mathematics
Use ruler and compasses for this question.
(i) Construct an isosceles triangle ABC in which AB = AC = 7.5 cm and BC = 6 cm.
(ii) Draw AD, the perpendicular from vertex A to side BC.
(iii) Draw a circle with center A and radius 2.8 cm, cutting AD at E.
(iv) Construct another circle to circumscribe the triangle BCE.
Answer
Steps of construction :
Draw a line BC = 6 cm.
Draw two arc intersecting each other at A having radius 7.5 cm and centre B and C.
Join AC and AB.
Draw perpendicular bisector of BC as AD.
With centre A and radius 2.8 cm, draw a circle which intersects AD at E.
Join EB and EC and draw perpendicular bisector of EB intersecting AD at O.
With centre O and radius OE or OB or OC draw a circle which passes through B and C and touches the first circle at E externally.
Hence, above is the required circle.
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