silly circle 2

Geometry Level 3

Two chords AB and CD of lengths 5 cm and 11 cm respectively of a circle are parallel and are on opposite sides of its centre. They are at a distance of 6 cm. If length of its radius is “n” cm find n√5?


The answer is 12.5.

Manish Mayank by Manish Mayank , 20, India

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2 solutions

Himanshu Arora
Jun 19, 2014

Imgur Imgur Make the two equations using Pythagorean Theorem : n 2 − x 2 = 25 4 n 2 − y 2 = 121 4 \\ n^{2} - x^{2} = \frac{25}{4} \\ n^{2} - y^{2} = \frac{121}{4} \\ and finally the last equation : x + y = 6 x+y=6

Solve the three equations to get n = 5 5 2 n= \frac{5\sqrt5}{2} \\ And hence the answer 12.5 \boxed{12.5} .

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i did the same

Parth Lohomi - 6 years, 11 months ago
Manish Mayank
May 21, 2014

Use following:

  1. radii of a circle are equal
  2. if sum of two no.s is 6 we can write the no.s as : n & (6-n)
  3. now use Pythagoras theorem and solving equation in two variables
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