Question

If in the following image AC is the diameter of the circle where AB = 4cm and BC = 1cm. Find the x?

Answer 1

Let AD=y and DC=z , in triangle ADC 25=y^2 + z^2

in triangle ADB y^2=x^2 + 16

in triangle BDC z^2=x^2 +1

solving we get 25=2x^2 + 17

     x=2

Answer 2

Ans: 2 cm

From the center of the circle, draw a radius (len = 2.5cm) to point D. Now you get a right angled triangle with the sides : x cm, 1.5 cm and 2.5 cm. Using Pythogoras, you get x^2 = 2.5^2 - 1.5^2 which gives x = 2 cm.

Answer 3

i have seen the other two answers. therefore another simple solution is as under:
if we complete the circle and draw mirror of x, applying one theorem of geometry x*x=4*1 or x=2

Comments

Could you detail this theorem?

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please refer to http://www.sparknotes.com/math/geometry2/theorems/section5/page/2/

Answer 4

X is the geometric mean of 4 and 1.
This is the square root of 4x1.
X therefore is 2.

Comments

No relationship with geometric mean here. And why not (4x1)/2 ?

Answer 5

Let us consider that the centre of the circle lies between A and Let it be O
Then join O and D
In the triangle DOB
OB =(2.5-1)
Do=radius=2.5cm
Therefore applying Pythagoras theorem
X^2+1.5^2=2.5^2
Solving we get x= 2cm