Question

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

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

Answer 1

 
Steps of construction:

1. Draw a line segment BC = 4 cm.
2. At C, draw a perpendicular line CX and from it, cut off CE = 2.5 cm.
3. From E, draw another perpendicular line EY.
4. From C, draw a ray making an angle of 45° with CB, which intersects EY at A.
5. Join AB.
6. ΔABC is the required triangle.
7. Draw perpendicular bisectors of sides AB and BC intersecting each other at O.
8. With centre O, and radius OB, draw a circle which will pass through A, B and C.
   Measuring the radius OB = OC = OA = 2 cm.