silly circle
Geometry
Level
2
In the figure, ∠LNM=100 degrees, where L,M and N are the points on a circle with center O. If ∠OLK = n degrees and ∠OLZ = 2n degrees, Find the ratio of KZ to LZ.
The answer is 0.5.
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1 solution
First you have to find "n" For this take any point,let X on the circle opp. to N.
Now in cyclic quadrilateral LNMX, angle LXM + angle LNM = 180 or,angle LXM = 80
Now, angle LOM = 2* angle LXM = 160 isosceles triangle LOM (as, OL=OM=r) n = 20/2 = 10
So angle KLZ = 3n = 30
and sin 30 degree = 1/2 = 0.5