Maharashtra State BoardSSC (English Medium) 9th Standard
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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. - Geometry

Diagram

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.

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Solution

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. Δ 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 Δ 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. Δ 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

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