Wednesday

October 22, 2014

October 22, 2014

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

- maths -
**Reiny**, Tuesday, February 12, 2013 at 8:14amlet 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. ...

Maths - ABC is a right angled triangle with ∠ABC=90∘ and side ...

calculas - find the perimeter of the rectangle with maximum area that can be ...

Geometry - ABC is a right angled triangle with ∠ABC=90∘ and side ...

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 ...

solid mensuration - Find the area of a portion of a semicircle of radius 15 m ...

Math - A Norman window has the shape of a rectangle surmounted by a semicircle...

Calculus 2 - how do I find the fluid force of a vertical semicircle that has ...

Math - Suppose that 600 meters of fencing are used to enclose a corral in the ...