Question

Construct incircle and circumcircle of an equilateral $∆$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

Steps of construction:
1. Draw a line SP = 7.5 cm.
2. With S as centre and 7.5 cm as radius, draw an arc above the line SP.
3. With P as centre and 7.5 cm as radius, cut an arc on on the previous drawn arc and name the point of intersection as D.
4. Join DS and DP. $∆$DSP is thus obtained.
5. Draw the perpendicular bisectors of the lines DP and SP. Let these perpendicular bisectors meet at point O.
4. With O as centre and OP as radius, construct a circle touching all the vertices of the $∆$DSP.
This circle is thus the required circumcircle.
Radius = 4 cm


Steps of construction
1. Draw a line SP = 7.5 cm.
2. With S as centre and 7.5 cm as radius, draw an arc above the line SP.
3. With P as centre and 7.5 cm as radius, cut an arc on on the previous drawn arc and name the point of intersection as D.
4. Join DS and DP. $∆$DSP is thus obtained.
5. Draw the angle bisectors of angle S and P and let them meet at point O.
6. Draw the perpendicular from point O to the line SP. Join OA.
7. With O as centre and OA as radius, draw a circle touching all the sides of the triangle.
This is the required incircle.
Radius = 2 cm
ratio of radius of circumcircle to the radius of incircle = 4 : 2 = 2 : 1