question_answer 1)

Let A and B be the centres of two circles of equal radii, draw them so that each one of them passes through the centre of the other. Let them intersect at C and D. Examine whether \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\] and \[{{l}_{4}}\] are at right angles.

Answer:

                To draw two circles such that each one of them passes through the centre of the other, we use the following steps: Step I Firstly, mark two points A and B on the paper. Step II Take the distance between A and B as radius and draw a circle with centre A Step III Now, take B as centre and draw a      circle with radius AB.   Thus, we get two circles which passes through the centres of each other. Let these circles intersect each other at C and D. Join C and D, which intersect AB at O. Then, we observe that, the \[{{l}_{1}}\] and \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] are equal to 90°. Hence, \[{{l}_{6}}\] So, we can say that \[{{l}_{1}},{{l}_{2}},{{l}_{3}},{{l}_{4}},{{l}_{5}}\] and \[{{l}_{6}}\] are at right angles.