top button
Flag Notify
    Connect to us
      Site Registration

Site Registration

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

0 votes
1,062 views

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

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

6 Answers

+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
answer 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.

answer 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

answer 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.

answer 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

answer Feb 20, 2017 by Sachite Anand
0 votes

In a rectangle triangle Base is always half of hight. Thus X will be 2 CMs.

answer Apr 20, 2019 by Subhash Gupta



Similar Puzzles
0 votes

In triangleABC, side AB = 20, AC = 11, and BC = 13. Find the diameter of the semicircle inscribed in ABC, whose diameter lies on AB, and that is tangent to AC and BC.

11-13-20 Triangle

0 votes

Triangle ABC has sides AB = 8, BC = 7, and AC = 9.
The segments AB and AC are extended and a circle O is constructed exterior to the triangle and is tangent to BC at D and the extended lines through AC and AB at N and M, as shown.
What is the radius of circle O?
enter image description here

+1 vote

If AF=1 and AB=AC=7 in the given image then what would be the radius of grey circle?

enter image description here

+3 votes

The figure shows an isosceles triangle with AB = BC. The line DE cuts AC extended at F. If AD=5, CE=3 and EF=8 find DE.

Find DE

+1 vote

If lengths of sides AB, BC and AC of a right angle triangle are in a geometric progression, what is the ratio between AC and AB?

Right Angle Triangle

...