+ R 2 where R 1. MULTIPLE CHOICE QUESTIONS (MCQ's) (Each question carries one mark)

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1 2. C h p t e r t G l n c e is the set of ll points in plne which re t constnt distnce from fixed point clled centre nd constnt distnce is known s rdius of circle. A tngent t ny point of circle is perpendiculr to the rdius through the point of contct nd the line perpendiculr to rdius of circle t its outer end is tngent to the circle. Two tngents cn be drwn from point outside the circle nd the lengths of such tngents re equl. If two circles re touching then the common point lies on the line joining their centres nd if the circles touch internlly the distnce between their centres is R 1 - R 2 nd if the circles touch externlly the distnt between centres is R 1 + R 2 where R 1 + R 2 re their rdii. The mesure of n ngle subtended by n rc t point on the circle is hlf of the mesure of the ngle subtended by the rc t the centre. An ngle subtended by semicircle t point on the circle is 90º Angles subtended by the sme rc re congruent A. The opposite ngles of cyclic qudrilterl CNC supplementry nd its converse is true. If n ngle with its vertex on the circle whose one side is tngent of circle nd other side is secnt then the mesure of the ngle is hlf of the mesure of the intercepted rc. If secnt is drwn through the point of contct of tngent to circle then the ngle which this tngent mkes with the chord contined the secnt re equl to the ngles subtended by the chord in the corresponding lternte segment. If two secnts of circle intersect inside or outside the circle then the re of the rectngle formed by the two line segments corresponding to one secnt is equl to re of the rectngle formed by the two line segments corresponding to other. If secnt nd tngent of circle intersect in point outside the circle then the re of the rectngle formed by the two line segments corresponding to the secnt is equl to the re of the squre formed by the line segment corresponding to the tngent. MULTIPLE CHOICE QUESTIONS (MCQ's) (Ech question crries one mrk) 1. A tngent t ny point of circle is... to the rdius through the point of contct. prllel b intersecting c perpendiculr d slnting 2. Three congruent circles with centres A, B nd C nd with rdius 5 cm touch ech other. Then perimeter of ABC is... cm. 15 b 20 c 30 d Rdius of the circle pssing through the vertices of right ngled tringle with sides 6 cm, 8 cm nd 10 cm is... cm. 3 b 4 c 5 d The opposite ngles of cyclic qudrilterl re.... supplementry b cute c obtuse d complementry

2 40 Unique MCQ's 5. Mesure of ngle inscribed in semicircle is º b 45º c 30º d 90º 6. A chord intersects circle in... points. one b mny c two d more thn two 7. The length of one tngent drwn from point outside circle is 7 cm the length of other tngent is... cm. 7 b 3.5 c 14 d Two circles with rdius 6 cm nd 4 cm touch ech other externlly the distnce between their centres is... cm. 5 b 24 c 6 d A chord divides circle is two rcs mesuring 2x nd 7x. The mesure of minor rc is º b 140º c 80º d 20º 10. An ngle subtended by semicircle t point outside the circle is... ngle. right b n cute c n obtuse d 180º 11. A cyclic prllelogrm is.... squre b rhombus c rectngle d kite 12. Angle subtended by sme rc re.... equl b unequl c congruent d cute 13. If two secnts of circle intersect in point 'P' then; AP BP = CP b AP = BP c CP = CD d AP BP = CP DP PD 14. The mesure of n inscribed ngle is... the mesure of the intercepted rc. Twice b hlf c one-fourth d equl 15. PQRS is cyclic qudritterl if m P = 4m R then m P =...? 36º b 144º c 9º d 46º 16. Mesure of n rc is equl to the mesure of...? inscribed ngle b semicircle c centrl ngle d circle 17. In the djoining figure, if m QPR = 50º, then m(rc QSR) =...? 25º b 80º c 100º d 130º 18. Two circles with centre P nd Q touch internlly. The rdius of smller circle is 8 cm. The distnce between their centre is 3 cm then find the dimeter of the lrger circle. 5 cm b 11 cm c 22 cm d 5.5 cm 19. A line which intersects the circle in two distinct points is clled... chord b tngent c secnt d rdius 20. In the djoining figure, if AD = 5, AB = 10 then OD =? 14 b 7.5 c 20 d 10

3 GEOMETRY - S.S.C (c) perpendiculr 2. (c) (c) 5 4. () supplementry 5. (d) 90º 6. (c) two 7. () 7 8. (d) (c) 80º 10. (b) n cute 11. (c) rectngle 12. (c) congruent 13. (d) AP BP = CP DP 14. (b) hlf 15. (b) 144º P + R = 180º [Opposite ngles of cyclic qudrilterl] 4 R + R = 180º 5 R = 180º R = = 36º P = 180º 36º = 144º 16. (c) centrl ngle 17. (d) m(rc QSR) = 130º Joing QO nd RO 1. Line QR is tngent t R. PQ = 13 cm, QR =12cm. Then rdius PR =... cm. 25 b 5 c 10 d 1 2. Q is the centre of circle. Answers Problems For Prctice OQP + ORP = 90º [Tngent perpendiculrity theorem] OQP + ORP = 90º + 90º = 180º PQRO is cyclic qudrilterl. QPR + QOR = 180º QOR = 180º 50º QOR = 130º QOR = m(rc QSR) [Centrl ngle property] m(rc QSR) = 130º 18. (c) D = 22 cm R r = 3 R 8 = 3 R = = 11 D = 2R = 2 11 = 22 cm 19. (c) secnt 20. (b) OD = 7.5 AB 2 = AD AC (10) 2 = 5 AC 100 = AC 5 AC = 20 CD = 20 5 = 15 OD = 1 CD 2 3. ABC is isosceles tringle with perimeter 34 cm. AB = AC nd BC = 10 cm. If circle touches the sides PM nd PN re tngents. If MPN = 50º then MQN = º b 100 c 130º d 310º of tringle, AP = cm b 5 cm c 7 cm d 10 cm 4. Two circles with centres P nd Q touch internlly. If their rdii re 10 cm nd 26 cm, then PQ =... cm. 16 b 36 c 13 d 6 = 1 15 = 7.5 2

4 42 Unique MCQ's 5. The rdii of two circles re 25 cm nd 9 cm nd CD = 34 cm AB = cm b 20 cm c 30 cm d 15 cm 6. If m(rc PMR) = 110º, then PQR = º b 55º c 60º d 120º 7. If m(rc AB) = 20º, m(rc CD) = 30º; then AMB = º b 30º c 50º d 25º 8. If BAC = 30 ; then m(rc BC) = b 60º c 30º d 10º 9. If BAC = 70º nd if rc intercepted by both the ngles is sme, PQR = º b 68º c 35º d 70º 10. If ABCD is cyclic; then.... = c b b = c c d = x d = x Answers 11. If m(rc PMQ) = 140º. Then PQR = º b 40º c 80º d 110º 12. seg AB nd seg AD re chords of the circle nd AC is tngent. If m(rc APB) = 70º, m(rc BQD) = 16º; then m CAD = º b 43º c 32º d 27º 13. seg PA is tngent nd seg PC is secnt. If AP = 12 cm, BP = 9 cm PC =... cm. 9 b 12 c 16 d In figure seg PB nd seg PD re secnt nd PA = 12 cm, PB = 15 cm, PC = 10 cm; then PD =... cm. 27 b 9 c 18 d In figure seg PT is tngent nd seg PB is secnt. PTA.... PAT b PBT c BPT d TAB 1 - b 2 - c 3 - c c 6 - b 7 - d 8 - b 9 - d 10 - d 11 - d 12 - b 13 - c 14 - c 15 - b

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