Using ruler and compasses only construct a triangle ABC in which BC 4 cm ACB 45 and the perpendicula...

Question

Using ruler and compasses only construct a triangle ABC in which BC 4 cm ACB 45 and the perpendicular from A on BC is 25 cm Draw the circumcircle of triangle ABC and measure its radius

Accepted Answer

Solution A circle that passes through each of the triangles vertices is known as the circumscribed circle or circumcircle of a triangle This circles circumcenter and circumradius are its centre and radius respectively Steps to construct Step 1 Draw a line segment BC 4cm Step 2 At point B draw a perpendicular and cut off BE 25cm Step 3 From E draw a line EF parallel to BC Step 4 From point C draw a ray making an angle 45o which intersects EF at point A Step 5 Join AB Step 6 Draw the perpendicular bisectors of sides BC and AC intersecting each other at point O Step 7 Join OB OC and OA Step 8 With O as the center and radius OB or OC or OA draw a circle which passes through points A B C Step 9 On measuring the radius OB 2cm

ML Aggarwal Solutions Class 10 Mathematics Solutions for Constructions Exercise 16.2 in Chapter 16 - Constructions