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Fig. 16.4, , are accustomed in using PQ to denote the line segment PQ and also its, ‘word radius will be used for the line segment joining the centre to any poi, , length., , us piece of acircle is called anarc of the circle., , Let P;, Po, Ps, Py, Ps, P, be points on the circle. Then, the pieces?), arcs of the circle C(O, r)., , a, , Fig. 16.5, , y, the circle is divided into Bade at |, in counter clockwise direction Y !, , ‘ ethearcfrom P to Q

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k Fig. 16.6, ote the length of arc Py 1(PO ), , lows from the above discussion that for a, , ny two points P and Q ona circle either, (PQ) < (QP) or 1(PQ) = 1 QP) or 1(PQ) > 1 By., , a (PQ) < 1(QP), then PQ is called the minor arc and OP is knownas the major arc. Thus,, , arcPQwillbe minor arc ot a major arc according as | (PQ) < (QP) or,, , CENTRAL ANGLE Let C(O, r) bean, angle., , I(PQ) > 1(QP). , y circle. Then any angle whose vertex is O is called the central, , a», , InFig. 16.7, Z POQ isacentral angle of the circle C(O, 7)., , Fig. 16.7, , We re-define the minor and major arcs of a circle by using the concept of central angle as, follows:, , MINOR ARC A minor arc of a circle is the, , collection of those points of the circle that lie on and also, insidea central angle., , In other words, a minor arc of a circle is a part of the circle intercepted by a central angle, including the two points of intersection., , MAJOR ARC A major arc of a circle is the collection of points of the circle that lie on or outside a, central angle., , i OP i j ircle., InFig. 16.7 PQ isaminorarcand QP isa major arc of the circ, a : i e, § Itis evident from the above discussion that the length of an arcis closely associated with the

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y j etermil The larger the central angle the larger wiy, %, , central angled ning the are Se eas ore beg am, , ne the ‘degree measure’ of an a of the central °° Min,, , We, therefore, define 8 ong, OF ANARC The degree measure of a minor are is the :, , Me che cent containing the arc and that of a major arc is, , re of the central angle ! h, 360° ed the degree measure of the corresponding minor arc., ted by mt (PQ)., , The degree measure ofanare PQ isdeno, , “Thus, if degree measure of an arc PO is 0° ,wewrite m (PQ) = &., P {a, , Clearly, m(PQ) + m(QP) = 360° or, m(PQ) + m(QP) = m(C(O, r)), , In Fig. 16.9, we have 2 Q, m(PQ) = 85° and m(QP) = 275° * |, , , , , , , Fig. 16.9 \, , 16.3 CHORD AND SEGMENT OF A CIRCLE, CHORD A line segment joining any two points ona circle is called a chord of the circle., , Itshould be noted that a chord is nota part of the circle., , DIAMETER A chord passing through the centre of.a circle is known as its diameter., Note that a circle has many diameters and a diameter of a given circle is one of the largest, , chords of the circle., REMARK The word ‘diameter’ will be used for a chord passing through the centre, and also forts, length., Clearly, if dis diameter of the circle C(O, r), then d = 2r. Also, itis evident that all diameterso!, acircle are equal., Pp P a Q, ee, Q PQ, Fig. 16.10 Fo teal, 16.1, SEMI-CIRCLE A diay oe at, weter of a circle divides it j ge 0”, sf a circle divides it into two equal parts which are arcs. Each of Hes, , arcs is called a semi-circle,