Distance of Chords from the Centre

Transcript

Distance of Chords from the Centre Here, we find relation between length of a chord and its distance from the centre. Before we jump into the theorems, let's clarify one very important rule in geometry: When we talk about the "distance" from a point to a line, we ALWAYS mean the shortest possible straight line, which is the perpendicular 90° line. Now, we have two theorems on this Theorem 6: Chords of a circle having the same length are all at the same distance from the centre of the circle. Intuitively If you take two sticks of the exact same length and wedge them into a ring, they have only one way they can fit. No matter where you slide them around the circle, they will always hover at the exact same distance from the center. Notice how they trace the edge of a hidden "inner circle" as you move them! No matter where you slide them around the circle, they will always hover at the exact same distance from the center. Notice how they trace the edge of a hidden "inner circle" as you move them! Let’s look at the Proof Proof is here Theorem 6 of Chapter 5 Class 9 – Ganita Manjari Part 1 Theorem 7: Chords of a circle that are equidistant from the centre have equal length Intuitively Imagine drawing a smaller "no-go zone" circle in the middle. If you draw lines that perfectly touch the edge of this inner circle (meaning they are the same distance from the center), those lines will always be chopped off at the exact same length by the outer ring! Let’s look at the Proof Proof is here Theorem 7 of Chapter 5 Class 9 – Ganita Manjari Part 1