Mathematics
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.
Answer
We know that a = BC, b = AC and c = AB.
Steps of construction :
Draw a line segment AB = 6 cm.
Construct ∠A = 30°. Extend segment from A to point C such that AC = 7 cm and ∠CAB = 30°.
Join C and B. Hence, △ABC is formed.
Draw perpendicular bisectors of AB and BC. Let these meet at O.
Now using O as centre and OA or OB as radius, draw a circle touching all the vertices of triangle ABC. This is the circumcircle of triangle ABC.
On measuring side BC we get, BC = 3.5 cm. Since a = BC,
∴ a = 3.5 cm.
Hence, the length of side a = 3.5 cm.
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 circle of radius 3 cm. Mark its centre as C and mark a point P such that CP = 7 cm. Using ruler and compasses only, construct two tangents from P to the circle.
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.
Using ruler and compasses only, construct an equilateral triangle of height 4 cm and draw its circumcircle.