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Circtes 179, , , , EXERCISE 10.4, G Two circles of radii 5 cm and 3 cm intersect at two points and the distance between, their centres is 4 cm. Find the length of the common chord., , 2. If two equal chords of a circle intersect within the circle, prove that the segments of, one chord are equal to corresponding segments of the other chord., 3. If two equal chords of a circle intersect within the circle, prove that the line, joining the point of intersection to the centre makes equal angles with the chords., 4. Ifaline intersects two concentric circles (circles, with the same centre) with centre O at A, B, C and, D, prove that AB = CD (see Fig. 10.25)., , 5. Three girls Reshma, Salma and Mandip are, , playing a game by standing on a circle of radius, , 5m drawn in a park. Reshma throws a ball to, , Salma, Salma to Mandip, Mandip to Reshma. If, , the distance between Reshma and Salma and A, , between Salma and Mandip is 6m each, what is, , the distance between Reshma and Mandip? Fig. 10.25, , 6. Acircular park of radius 20m is situated in a colony. Three boys Ankur, Syed and, David are sitting at equal distance on its boundary each having a toy telephone in, his hands to talk each other. Find the length of the string of each phone., , 10.7 Angle Subtended by an Arc of a Circle, , You have seen that the end points of a chord other than diameter of a circle cuts it into, two arcs — one major and other minor. If you take two equal chords, what can you say, about the size of arcs? Is one arc made by first chord equal to the corresponding arc, made by another chord? In fact, they are more than just equal in length. They are, congruent in the sense that if one arc is put on the other, without bending or twisting,, one superimposes the other completely. D, , You can verify this fact by cutting the arc,, corresponding to the chord CD from the circle along, CD and put it on the corresponding arc made by equal, chord AB. You will find that the arc CD superimpose A IC, the arc AB completely (see Fig. 10.26). This shows, that equal chords make congruent arcs and, conversely congruent arcs make equal chords of a, circle. You can state it as follows:, , If two chords of a circle are equal, then their corresponding ares are congruent, and conversely, if two arcs are congruent, then their corresponding chords are, , equal. ; i“, , B, Fig. 10.26