Using a ruler and a pair of compasses only, construct: (i) A triangle ABC given AB = 4 cm, BC = 6 cm and ∠ABC = 90°. (ii) A circle which passes through the points A, B and C and mark its centre as O. (2008)
Using a ruler and a pair of compasses only, construct: (i) A triangle ABC given AB = 4 cm, BC = 6 cm and ∠ABC = 90°. (ii) A circle which passes through the points A, B and C and mark its centre as O. (2008)

Solution:

Steps to construct:

Step 1: Draw a line segment AB = 4cm.

Step 2: At point B, draw a ray BX making an angle of 90o and cut off BC = 6cm.

Step 3: Join AC.

Step 4: Draw the perpendicular bisectors of sides AB and AC intersecting each other at point O.

Step 5: With center as O, and radius equal to OB or OA or OC, draw a circle which passes through points A, B, C.