Question

Construct incircle and circumcircle of an equilateral Δ DSP with side 7.5 cm. Measure the radii of both the circles and find the ratio of radius of circumcircle to the radius of incircle.

Answer 1

Rough figure:

Steps of construction:

1. Construct ∆DPS of the given measurement.
2. Draw the perpendicular bisectors of side DP and side PS of the triangle.
3. Name the point of intersection of perpendicular bisectors as C.
4. Join seg CP.
5. Draw a circle with centre C and radius CM.
6. Draw a circle with centre C and radius CP.

Radius of incircle = 2.2 cm

Radius of circumcircle = 4.4 cm

`"Radius of circumcircle"/"Radius of incircle" = 4.4/2.2 = 2/1`

∴ CP : CM = 2 : 1