Given:
m(ar KN) = 2x + 151
m(ar LN) = 61°
m∠NMK = 2x + 45
To find:
m∠NMK
Solution:
By property of circle:
<em>If a tangent and a secant intersect outside a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.</em>
Multiply by 2 on both sides, we get
Subtract 90 from both sides.
Subtract 2x from both sides.
Substitute x= 0 in m∠NMK.
m∠NMK = 2x + 45
= 2(0) + 45
= 45
Therefore m∠NMK = 45.
Answer:
1 The ratio of the measure of the central angle to the measure of the entire circle is StartFraction 5 Over 2 pi EndFraction
3 The area of the sector is 250 units².
5 The area of the sector is more than half of the circle’s area
We are asked in the problem to determine the number of quarters that are needed to complete 4975 units given the equation y = x6 − 25x4 + 199x2 where y is the number of manufactured units and x is the number of quarters needed.
substituting y = 4975, we find x. <span>x is readily found using calculator.</span>
We know that
if <span>points a and b lie on the circle and O is the center
so
OA is the radius
OA=OB
5x-11=4(x-1)-----> 5x-11=4x-4----> 5x-4x=11-4-----> x=7
OA=5x-11-------> OA=5*7-11-----> OA=24 units
the diameter is (OA+OB)
2*OA------> 2*24------> 48 units</span>
