Using ruler and compass construct a triangle ABC where AB = 3 cm, BC = 4 cm and ∠ABC = 90°. Hence construct a circle circumscribing triangle ABC. Measure and write down the radius of the circle.

Construction:

1. Draw BC = 4 cm.
2. At B, construct a perpendicular to BC.
3. On this perpendicular, mark A such that AB = 3 cm.
4. Join AC. This gives right triangle ABC with ∠ABC = 90°.
5. Construct the perpendicular bisector of AC and locate its midpoint O.
6. With O as centre and OA as radius, draw the circle through A, B and C.

Since ABC is a right-angled triangle, AC is the diameter of its circumcircle.

AC = √(AB² + BC²)

= √(3² + 4²)

= 5 cm

Radius = AC/2

= 5/2

= 2.5 cm

Answer:

Radius of the circumscribed circle = 2.5 cm.

In a right triangle, the midpoint of the hypotenuse is equidistant from all three vertices. Therefore the circumcentre is the midpoint of AC and the circumradius is half the hypotenuse.