The radius of two circles is 20 cm and 18 cm. Both circles inters
| The radius of two circles is 20 cm and 18 cm. Both circles intersect each other at two points and the length of their common chord is 16 cm. Then, what is the distance between their centres (in cm)?
A. <span class="math-tex">\(\left( {4\sqrt {21} + 2\sqrt {65} } \right)\)</span>
B. <span class="math-tex">\(\left( {4\sqrt {21} + 3\sqrt {65} } \right)\)</span>
C. <span class="math-tex">\(\left( {3\sqrt {21} + 2\sqrt {65} } \right)\)</span>
D. <span class="math-tex">\(\left( {2\sqrt {21} + 4\sqrt {65} } \right)\)</span>
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Given, CD = 16 cm
∴ CE = 16/2 = 8 cm
Now, in ΔACE
AE2 = AC2 - EC2
⇒ AE2 = (20)2 - 82
⇒ AE2 = 400 - 64
⇒ AE2 = 336
⇒ AE = √336
⇒ AE = 4√21 cm
In ΔCEB
EB2 = CB2 - CE2
⇒ EB2 = 182 - 82
⇒ EB2 = 324 - 64
⇒ EB2 = 260 cm
⇒ EB = 2√65 cm
∴ The distance between the centre (AB) = AE + EB = (4√21 + 2√65) cm
