Question 3 - Think & Reflect (Page 95) - Number of Circles - Chapter 5 Class 9 - I’m Up and Down, and Round and Round (Ganita Manja

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Question 3 - Think & Reflect (Page 95) As you move away from segment AB along its perpendicular bisector, do the radii of the circles containing A and B increase or decrease? Let’s make a diagram Let M the mid-point of the circle And, O be the center of the circle which is away from line segment AB Now, if center is on line segment AB (like point M) Then, Radii if we are line segment AB = 𝟏/𝟐 × AB We need to find Radii if we are away from line segment AB i.e. we need to find OB Now, ∆ OMB is a right angled triangle Applying Pythagoras Theorem 𝑶𝑩^𝟐=𝑶𝑴^𝟐+𝑴𝑩^𝟐 Putting MB = 1/2 × AB 𝑂𝐵^2=𝑂𝑀^2+(1/2 𝐴𝐵)^2 𝐎𝐁=√(𝑶𝑴^𝟐+(𝟏/𝟐 𝑨𝑩)^𝟐 " " ) Since something is added to (𝟏/𝟐 𝑨𝑩)^𝟐 and then taken square root It means it is bigger than 𝟏/𝟐 𝑨𝑩 Thus, radii increase as we move away from AB Let’s take an example