Question

If M = N, the diameter of M = 148, and AB = 140, what is the length of NQ?

Answer 1

`NQ=24\ units`

Explanation:

we know that

Triangles ABM and CDN are congruent

so

CD=AB

AB=2AL ----> because the diameter divide the circle into two equal parts

CQ=AL=140/2=70 units

NC----> is the radius

NC=148/2=74 units ----> the radius is half the diameter

Applying Pythagoras Theorem find the value of NQ

`NC^(2)=NQ^(2)+CQ^(2)`

substitute the values

`74^(2)=NQ^(2)+70^(2)`

`NQ^(2)=74^(2)-70^(2)`

`NQ^(2)=576`

`NQ=24\ units`