In the diagram in the left below, AD is a diameter of the circle and is tangent to line m at D. If AD=1 AND BC is perpendicular to m, show that:
a) AB + BC = 1 +cos(x) - cos^2(x)
b) What value of x makes the sum AB + BC a maximum?
In the diagram in the left below, AD is a diameter of the circle and is tangent to line m at D. If AD=1 AND BC is perpendicular to m, show that:
a) AB + BC = 1 +cos(x) - cos^2(x)
b) What value of x makes the sum AB + BC a maximum?
Hello, violetice!
is isosceles withis a diameter of circle and is tangent to line atCode:A * * * * |x * * * | * * * E + - - - -* B | * | * |θ * |* * O* |* * | |* | | * | * * | *| * | * | - - - - * * * - - -+- - - - m D C
If and ,
. . a) show that: .
Then: .
Law of Cosines: .
We have: .
. .
We see that: .
In right triangle
Hence: .
Therefore: .
b) What value of makes the sum a maximum?
We have: .
Differentiate and equate to zero: .
. . Factor: .
We have: . . This gives a minimum sum.
And: .