Question

Using ruler and compass construct a triangle ABC where AB = 3 cm, BC = 4 cm and
ZABC90°Hence construet a circle circumscribing the triangle ABC. Measure and
write down the radius of the circle.​

Answer 1

The construction of triangle ABC where AB = 3 cm, BC = 4 cm and  ZABC90° using ruler and compass is as shown below.

Steps of construction:

Draw a line BC with a scale of 4 cm using the ruler.

From point B draw a line perpendicular to the line BC (as given, ∠ ABC = 90°) with a scale of 3 cm.

Mark the other point as A.

Join AC.

From points B and C draw arcs above and below the line BC and join the intersection of the arcs.

From points A and B draw arcs above and below the line AB and join the intersection of the arcs.

From points A and C draw arcs above and below the line AC and join the intersection of the arcs.

A point where all the above lines meet is the center of required circle and mark it as O.

With center O and radius equal to OA or OB or OC draw a circle.

Hence the required construction.