BOOK II.

1. If the radii of two intersecting are 3" and "7" respectively, what is the greatest possible distance, in feet and inches, between their centres? The least?

2. Four chords are 2Km 5Dm gdm, 0.15 miles, 0.25Km, and 330 yards, respectively. If one is a diameter, which is it? Which of the others is nearest to the centre? Which farthest from it?

3. If a central of 28° intercepts an arc of 3.2", find, in feet and inches, the arc intercepted by an equal equal .

in an

4. What can you say of the central of a ○ which intercept, and the chords which subtend, two arcs which are respectively 28 yards and 25 ?

5. In a given O, the chord A B is 5 yards 2 feet, the chord C G is 4.9m. Compare the arcs A B and C D, and the distances of the chords from the centre.

6. What can you say of two chords whose distances from the centre are 13cm and 5 inches respectively?

7. One of the arcs intercepted by two chords, one of which is a diameter, intersecting at right angles, is 41° 18′ 4′′; find the other arcs.

8. A secant parallel to a tangent subtends an arc of 117° 41'; find the arcs intercepted by the secant and the tangent.

9. One of the arcs intercepted by a diameter and a parallel secant is 37° 30'; find the length, in miles, of the

arc subtended by this secant, if a degree of the circumference is 24Km. (Log.)

10. The line joining the centres of two, tangent to each other externally, is 14m 7am 3cm, and the radius of the less is 3m 8dm 5cm, find the radius of the greater.

11. If a central of 25° 15' intercepts an arc of 15 feet 10 inches, find the length of the semi-circumference of the O. (Log.)

12. How many degrees in an inscribed in of a circumference?

13. Find the length of the arc intercepted by an inscribed of 20° 22' in a O whose circumference is of a mile. (Log.)

14. How many degrees in an inscribed which intercepts of a quadrant?

15. Anformed by a tangent and a chord is; how many degrees in the intercepted arc ?

16. Find the length of the arc intercepted by a central of 12° 15' in a whose circumference = 1Km. (Log.)

17. If a central

of 85° 40′ intercepts an arc of 32.5m, how many degrees and minutes in the central which in

18. What part of a is an / between a tangent and a chord intercepting an arc of of a semi-circumference?

19. The between two chords intersecting within the circumference is 35°, its intercepted arc is 25° 18′; find the arc intercepted by its vertical .

20. Find the between a secant and a tangent when their intercepted arcs are respectively and of the circumference.

21. The between two secants, intersecting without the circumference, is 58° 41', one of the intercepted arcs is 230°; find the other.

22. Find the between two tangents when the intercepted arcs are in the ratio 7: 2.

FIG. 2.

W

H

FIG. 3.

M

23. If, in Fig. 2, the A B C = 67°, and the arc D C is 25°, how many degrees in the ABD?

24. In the same figure, B G is a diameter, B C is 8° more than G C ; find the E B C.

25. In the same figure, the arc D B is three and onehalf times the arc D C, and the D B G = 131°; find the DB C.

:

26. In the same figure, if G D and B C are in the ratio 3 and the D B C = 15°, how many degrees in the GBC?

L

27. In Fig. 3, Q P is 24° less than a semi-circumference, how many degrees in the QM P?

28. The R M K is 27°, the arc R K is 100°; how long is the arc T L, if a quadrant on this figure = 15m ?

29. The R H K is 70°, the arc RQL is three times as long as the arc K P; find the number of degrees in K P.

30. The arc R P T is 10° less than two-thirds of a circumference, the Q M T is 17°; how many degrees in QT?

31. How many degrees in the central which intercepts an arc of 17cm, when a quadrant is 4dm 2cm 5mm ?

32. The between two tangents from the same point is 32° 30'; find the ratio of their intercepted arcs.

33. If a central of 65° intercepts an arc of 10 feet 5.984 inches, how many metres will there be in an arc of the same intercepted by a central of 211° 15'? (Log.) 34. The

to a

between two tangents from the same point, whose radius is 55cm, is 120°; how many inches in the chord joining the points of tangency?

35. The centres of two which are tangent to each other internally are 5 feet 8 inches apart, the radius of one is 1.1"; find the radius of the other.

of 17°

36. The chord joining the points of tangency of two intersecting tangents forms with one of them an 7; find the between the tangents.

37. The radii of two concentric are 8 feet 2.425 inches and 2.25m, respectively; find the radius of a tangent to both. (Two solutions.) Get one answer in metric units, the other in English units.

38. The between two chords, one of which is a diameter, is; find the arc subtended by the less chord.

39. Find the circumference, in metres, of a in which

a central of 11° 15′ intercepts an arc of 3.5 inches. (Log.)

40. The between a tangent and a secant is 8° 11', the smaller of the intercepted arcs is 56° 50′ 40′′; find the larger.

41. In a certain a central of 78° 45′ intercepts an arc of 168 miles; how long will it take a train moving 24 miles per hour to cover the circuit ?

42. Two sides of an inscribed ▲ subtend the circumference, respectively; find the

43. One of an inscribed is 35°, subtends an arc of 113°; find the other

and of of the ▲.

one of its sides of the A.

arcs of 100° and and the made by the non

44. The bases of a trapezoid subtend 140°, respectively; find its parallel sides produced.

45. How long would it take a train running 40 miles an hour to go round a O in which a central of 15° intercepts an arc of 7.2Km? (Log.)

46. The numbers of degrees in the arcs subtended by the sides of a pentagon, in order, are consecutive; find the of the pentagon.

47. The arcs subtended by three consecutive sides of a quadrilateral are 87°, 95°, 115°; find the of the quadrilateral; the made by the intersection of the diagonals; and the made by the opposite sides of the quadrilateral, when produced.

48. Find the made by the radii and the line joining the points of contact of two tangents drawn through a