Question

on the diagram below how would i work out the length of the arc from A to B via C

Answer 1

(the distance betwean a and b is 8 on the straight line btw

Answer 2

there is not information given to calculate the length of the arc. you need to know the radius of the circle as well. Or the angle subtended at the centre by the chord AB.

Answer 3

wts the radius?

Answer 4

sorry the radius is 8

Answer 5

and whts the distance>?

Answer 6

cm

Answer 7

the angle at centre is arcsin 1/2 * 2 = 60 dgrees = pi/3 in radians
small arc is of length 8 * pi/3

large arc = 2*pi * 8 - 8*pi/3 = 41.89 cm

Answer 8

thanks but i dont understand how you got the small arc

Answer 9

ok - well i' imagined' the small arc the other side of AB - which will complete the circle.
then the length of large arc AB = perimeter of the circle - length of small arc

Answer 10

trust me lol!

Answer 11

yh i know the how to get the arc if i know the small arc but in future if i get a question like this i nead to know how to work hout the small arc

Answer 12

wouldnt you work out the distance betwean line AB and take that away from the perimiter ehich equals 14.73 and then times by pi and that s the answer

Answer 13

46.3

Answer 14

no the length of small arc = radius * angle at centre (with angle measuredin radians)

Answer 15

if u imagine a full circle the angle subtended by chord at centre is
\[2*\sin^{-1} (1/2)\] = 60 ... ap thts 1/6 of the perimeter is cut of .. so the remainin length is \[5/6*2*8*\Pi\]

Answer 16

oh ok kl thanks guys

Answer 17

thts 41.87 approx

Answer 18

ok - yes dk thats another way to do it