construct a triangle ABC similar to given equilateral triangle PQR with side is 6/7th of the coresponding side of triangle - Maths - Constructions

Question

construct a triangle ABC similar to given equilateral triangle PQR
with side is 6/7th of the coresponding side of triangle PQR, Also
draw the circumcircle of triangle ABC write the steps of
constructions

Vijay Kumar Gupta · Accepted Answer

Dear student,

Please find below the solution to the asked query:

Follow the following steps of construction:1
 First construct an equilateral triangle PQR taking QR as base
2
 Draw a ray QX which is inclined at an acute angle with QR
3
 Mark 7 points on ray QX at an equal distances frome each other
Let these points be X1, X2, X3, X4, X5, X6, X74
 Join RX7 5
 From  X6, draw a line parallel to RX7 intersecting QR at point C
6
 Again from this point C, draw a line parallel to PR which intersects PQ at point AThen △AQC is the required similar triangle
Now to draw a circumcircle of thsi triangle, follow the following steps:7
 Draw perpendicular bisectors of  any two sides of this triangle, say AC and AQLet these intersect at point O
8
 With O as center and radius equal to OA, draw a circle
This circle passes through the three vertices of △ and is the required circumcircle
The figure is shown below:

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construct a triangle ABC similar to given equilateral triangle PQR with side is 6/7th of the coresponding side of triangle PQR, Also draw the circumcircle of triangle ABC. write the steps of constructions.