Mathematics
Using ruler and compasses only, construct an equilateral triangle of height 4 cm and draw its circumcircle.
Answer
Steps of construction :
Draw a line XY and take a point D on it.
At D, draw perpendicular and cut off DA = 4 cm.
From A, draw rays making an angle of 30° on each side of AD meeting the line XY at B and C.
Now draw perpendicular bisector of AB intersecting AD at O.
With centre O and radius OA or OB or OC, draw a circle which will pass through A, B and C.
This is the required circumcircle of △ABC.
Related Questions
Using ruler and compasses only :
(i) Construct a triangle ABC with the following data :
BC = 7 cm, AB = 5 cm and ∠ABC = 45°.
(ii) Draw the inscribed circle to △ABC drawn in part (i).
Draw a line AQ = 7 cm. Mark a point P on AQ such that AP = 4 cm. Using ruler and compasses only, construct :
(i) a circle with AP as diameter
(ii) two tangents to the above circle from the point Q.
Draw a triangle ABC, given that BC = 4 cm, ∠C = 75° and that radius of circumcircle of △ABC is 3 cm.
Using ruler and compasses only, construct a triangle ABC having given c = 6 cm, b = 7 cm and ∠A = 30°. Measure side a. Draw the circumcircle of the triangle.