Question

A chord ab makes an angle of 30 at a point c on the circle. if the radius of the circle is 4 cm , find the length of the chord

Answer 1

first draw a figure

for this draw a circle and draw a chord in it named AB join A to the center of the circle as well as B we will obtain a equilateral triangle the draw angle in major arc as well as in minor arc. name the center of the circle as o and angle in major arc name it as D and in minor arc as E.

so, solu. is this

in triangle AOB

angle AOB+ABO+BAO=180

AS it is an equilateral triangle

so all the angles will be 60 degree

so angle subtented by an arc at the centre is double of the angle in any part of the circle

angle AOB=2angle ADB

angle ADB=60/2=30 degree

so we get the angle in major arc

if u look in the figure we get the AEBDis a cyclic quad.

so angle AOB+ angleAEB=180

so angle AEB=180- angle ADB

angle AEB= 150 degree this is the angle in minor arc

so this is the solu.