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: .