Ex 5.1, 1 (iv) - Chapter 5 Class 9 Introduction to Euclid's Geometry

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Ex 5.1, 1 (Method 1) Which of the following statements are true and which are false? Give reasons for your answers. (iv) If two circles are equal, then their radii are equal. Two circles are equal means that region bounded by circle is same. On superimposing the region bounded by one circle on the other circle if the circles coincide. We observe their centres and boundaries coincide. Therefore, their radii will be equal. So, true. Ex 5.1, 1 (Method 2) Which of the following statements are true and which are false? Give reasons for your answers. (iv) If two circles are equal, then their radii are equal. Let radius of first circle be r1 & radius of second be r2 Since, two circles are equal Area of circle 1 = Area of circle 2 πr12 = πr22 r12 = r22 ⇒ r1 = r2 Since, r1 = r2 Radius of two circles are equal Therefore, their radii will be equal.