Question

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

Answer 1

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, 2 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.

Answer 2

S O L U T I O N :

☆ Steps of Construction : ☆

1. Dram BC = 4 cm.

2. Make an angle of 90° at B and cut an arc of radius 3 cm on it to get point A.

3. Join AC. Thus△ABC is obtained.

4. Draw perpendicular bisector of AC, which meets AC at D.

5. Taking D as centre and radius equal to AD or DC, draw a circle. Thus, it is required circle.

• Since, AB = 5 cm, So, AD = 2.5 cm.

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