circle question

I think 2pi minor arc, or 34pi major arc

If the chord were to be 18 i.e 3 times of what it is right now.. than arc AB would be 1/6*circumference of circle.. coz the angle subtended would be 60

now since it is 6, so we need to divide it by 3, so now the arc is 1/18 of the circumference..

so 2pi.. = minor arc..
and 34pi = major arc..

am getting the length of the minor arc AB as 9pi

if we extend the radius from the center O to B, we get the diameter, join AC, angle CAB=90 (the diameter makes a 90 degree at the circumference)

so CAB is a right angled triangle, OC=OB (radius)=>AO is perpendicular to the diameter CB
(in a right angled traingle, a perpendicular drawn from the point of the 90 degree angle to the hypotanuse bisects the hypotanuse)

so length of minor arc AB:
2*pi*18*90/360=9pi.

scoobydooby wrote:am getting the length of the minor arc AB as 9pi

if we extend the radius from the center O to B, we get the diameter, join AC, angle CAB=90 (the diameter makes a 90 degree at the circumference)

so CAB is a right angled triangle, OC=OB (radius)=>AO is perpendicular to the diameter CB
(in a right angled traingle, a perpendicular drawn from the point of the 90 degree angle to the hypotanuse bisects the hypotanuse)

so length of minor arc AB:
2*pi*18*90/360=9pi.

Doesnt seem possible to me.. if length is 9pi that would mean that the angle subtended by the arc to the center is 90 degrees.. that is impossible.. coz the chord is the hypotenuse here.. longest side in a triangle.. and here it is not longest.. coz the radius itself is 18

your diagram is also incorrect.. although it would be a right angle that a diameter subtends on the perimeter of a circle.. the way you have drawn is incorrect..

OA please

yes, you are correct dumb.doofus. my solution does not seem possible at all