If in the following image AC is the diameter of the circle where AB = 4cm and BC = 1cm. Find the x?
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
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.
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
X is the geometric mean of 4 and 1.
This is the square root of 4x1.
X therefore is 2.
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
Therefore applying Pythagoras theorem
Solving we get x= 2cm
In a rectangle triangle Base is always half of hight. Thus X will be 2 CMs.
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