Question

The acute angle at which the circles (x – 1)2 + (y – 4)2 = 1 and x2 + (y – 2)2 = 5 intersect is k° then k is divisible by

Answer 1

Given :   (x – 1)² + (y – 4)² = 1     and  x² + (y – 2)² = 5

To Find : acute angle  at which circle intersects

Solution:

(x – 1)² + (y – 4)² = 1  

center = ( 1 , 4)

radius = 1

x² + (y – 2)² = 5

center = ( 0 , 2)

 radius = √5

Distance between centers

( 1 , 4) and ( 0 , 2)

= √(1 - 0)² + (4 - 2)²

= √5

AB² = AC² + BC² - 2AC.BC.Cosα

=> 5 = 1 + 5 - 2(1)√5Cosα

=> Cosα = 1/2√5

=>  α =  77.08°

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