Using ruler and compasses only construct a triangle ABC in which BC = 4 cm, ∠ACB = 45o and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC.
Using ruler and compasses only construct a triangle ABC in which BC = 4 cm, ∠ACB = 45o and perpendicular from A on BC is 2.5 cm. Draw a circle circumscribing the triangle ABC.

Steps for Construction:

i) Draw a line segment BC = 4 cm.

ii) At C, draw a perpendicular line CX and from it, cut off CE = 2.5 cm.

iii) Draw another perpendicular line EY from E.

iv) From C, draw a ray making an angle of 45o with CB, which intersects EY at A.

v) Join AB.

Then, ΔABC is the required triangle.

vi) Draw perpendicular bisectors of sides AB and BC intersecting each other at O.

vii) With centre O, and radius OB, draw a circle which will pass through A, B and C.

Therefore, the radius OB = OC = OA = 2 cm.

Selina Solutions Concise Class 10 Maths Chapter 19 ex. 19 - 9