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Question
Construct the circumcircle and incircle of an equilateral ∆XYZ with side 6.5 cm and centre O. Find the ratio of the radii of incircle and circumcircle.
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Solution
Steps of Construction (to draw the circumcircle):
1. Draw an equilateral triangle ABC with each side 6.5 cm.
2. Draw the perpendicular bisectors of AB and BC. Let these meet at the point O.
3. With O as centre and OB as radius, draw a circle. This circle is the circumcircle of triangle ABC.
Steps of Construction (to draw the incircle):
1. Draw the angle bisectors of \[\angle\]CAB. It passes through the point O.
2. From point O, draw a perpendicular on AB. Let this meet AB in D.
3. With O as centre and OD as radius, draw a circle. This circle is the incircle of triangle ABC.
\[\frac{Radius\ of\ incircle}{Radius\ of\ circumcircle} = \frac{2}{4} = \frac{1}{2}\]
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