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

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

find x

posted Jun 26, 2015 by Kuldeep Apte

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5 Solutions

+4 votes
 
Best answer

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
solution Jun 26, 2015 by Ankit Kamboj
+2 votes

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.

solution Jun 27, 2015 by anonymous
+1 vote

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

solution Jul 7, 2015 by Kewal Panesar
Could you detail this theorem?
0 votes

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

solution Jul 27, 2015 by anonymous
No relationship with geometric mean here. And why not (4x1)/2 ?
0 votes

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

solution Feb 20 by Sachite Anand



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