Posted by **harsh** on Tuesday, February 12, 2013 at 5:40am.

A semicircle has AB as the endpoints of its diameter, and AB=400. Points C and D are on the circumference of the semicircle such that AD=BC=100. What is the length of DC?

- maths -
**Reiny**, Tuesday, February 12, 2013 at 8:14am
let your centre be O.

Join OD and OC

Triangles AOD and BOD are clearly congruent (SSS)

let's look at triangle BOD, with sides 200, 200 , 100

and its central angle BOD = Ø

A "similar" triangle 2 , 2, 1 has the same angle Ø

by cosine law:

1^2 = 2^2 + 2^2 - 2(2)(2)cosØ

8cosØ = 7

cosØ = 7/8

It can be easily seen that CD || AB

so in triangle COD we have angle ODC = Ø

Let CD = 2x, draw an altitude from O to meet CD at P

clearly P is the midpoint, OPD is right-angled and

x/200 = cosØ

x = 200cosØ = 200(7/8) = 175

then 2x or CD = 350

## Answer This Question

## Related Questions

- geometry - A semicircle has AB as the endpoints of its diameter, and AB=80. ...
- calculas - find the perimeter of the rectangle with maximum area that can be ...
- Maths - ABC is a right angled triangle with ∠ABC=90∘ and side ...
- Geometry - ABC is a right angled triangle with ∠ABC=90∘ and side ...
- math - Figure WXYZ is a rectangle with a semicircle added to its base. What is ...
- Calculus - Find the rectangle of largest area that can be inscribed in a ...
- pre-calc - a semicircle of radius r=3x is inscribed in a rectangle so that the ...
- Calculus - A rectangle is constructed with its base on the diameter of a ...
- calculus - A rectangle is constructed with its base on the diameter of a ...
- Calculus - Find the area of the largest rectangle that fits inside a semicircle ...

More Related Questions