Name: Ruler and Compass Constructions
Uploaded: 2019-07-19
Duration: 9 min 30 s

Question

Construct an incircle and a circumcircle on an equilateral triangle, now calculate the incircle and circumcircle. Are both of them located at the same point?

Accepted Answer

(i)Draw a line SP=7.5 cm
(ii) With S as centre and 7.5 cm as radius, draw an arc above the line SP
(iii) With P as centre and 7.5 cm as radius, cut an arc on the previous drawn arc and name the point of intersection as D.
(iv)Join DS and DP △DSP is thus obtained
(v)Draw the perpendicular bisectors of the lines DP and SP. Let these perpendicular bisectors meet at point O.
(vi)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
(i) Draw a line SP=7.5cm
(ii) With S as centre and 7.5 cm as radius, draw an arc above the line SP
(iii) 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
(iv) Join DS and DP △DSP is thus obtained
(v) Draw the perpendicular from point O to the line SP. Join OA
(vi) With O as centre and OA as radius, draw a circle touching all the sides of the triangle this is the incircle
Radius =2cm
ratio of radius of circumcircle to the radius of incircle =4:2=2:1

Construct an incircle and a circumcircle on an equilateral triangle, now calculate the incircle and circumcircle. Are both of them located at the same point?

Important Questions on Geometrical Constructions

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