Question 1 - Think & Reflect (Page 93) - Definitions - Chapter 5 Class 9 - I’m Up and Down, and Round and Round (Ganita Manja

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Question 1 - Think & Reflect (Page 93) Jamuna has a circular piece of paper. She is trying to locate its centre. Amina gives her a suggestion. She follows the instructions and is thrilled to find that it works. Can you guess what Amina told her? We have to find Center any Circle Here, we use the logic Perpendicular bisector of a chord passes through center Thus, we Make chords of the given circle Draw perpendicular bisectors Where the perpendicular bisectors meet is the center Let’s do it step-by-step The Target Circle Here is our circle. Its center is currently unknown to us. Our goal is to find its exact center using basic geometric principles. Previous STEP 1 / 11 Next StepDraw First Chord Draw a straight line segment connecting any two distinct points on the circle. Let's label the endpoints A and B. Previous STEP 2 / 11 Next StepFind the Midpoint Find the exact midpoint of chord AB . Let's mark this point as M 1 . Previous STEP 3 / 11 Next StepDraw Perpendicular Using a protractor, measure exactly 90 degrees from the chord at M 1 and draw a straight line. Geometry tells us the center must lie somewhere on this line. Previous STEP 4 / 11 Next StepDraw Second Chord Now, draw a second, completely different chord connecting two other points on the circle. Let's call them C and D. Previous STEP 5 / 11 Next StepMidpoint of Second Chord Find the exact midpoint of chord CD and mark it as M 2 . Previous STEP 6 / 11 Next StepDraw 2nd Perpendicular Use a protractor to draw a 90-degree line through M2. The circle's center must be on this line too, so the intersection point looks promising! Previous STEP 7 / 11 Next StepDraw a Third Chord To definitively prove our intersection point is correct, let's draw a third chord connecting points E and F. Previous STEP 8 / 11 Next StepMidpoint of Third Chord Find the exact midpoint of chord EF and mark it as M3. Previous STEP 9 / 11 Next StepDraw 3rd Perpendicular Draw a 90 -degree line through M3. Notice exactly where this third line passes. Previous STEP 10 / 11 Next StepCenter Found! All three perpendicular bisectors intersect perfectly at a single location. This intersection is the true center of the circle. Previous STEP 11 / 11 Finished