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The circle centered at (2,-1) and with radius 4 intersects the circle centered at (2,-5) and with radius sqrt(10) at two points A and B. Find (AB)^2

 Jun 26, 2021

Best Answer 

 #1
avatar+1540 
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The circle centered at (2,-1) and with radius 4 intersects the circle centered at (2,-5) and with radius sqrt(10) at two points A and B. Find (AB)2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PR = 4         PQ = 4 - QR

 

(BP)2 - (PQ)2 = (BR)2 - (QR)2

 

42 - (4 - QR)2 = 10 - (QR)2

 

QR = 11/4          (PQ = 23/4)

 

AB = 2{sqrt[(BR)2 - (QR)2]}            

 

(AB)2 = 333/4

 

 Jun 26, 2021
 #1
avatar+1540 
+4
Best Answer

The circle centered at (2,-1) and with radius 4 intersects the circle centered at (2,-5) and with radius sqrt(10) at two points A and B. Find (AB)2

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PR = 4         PQ = 4 - QR

 

(BP)2 - (PQ)2 = (BR)2 - (QR)2

 

42 - (4 - QR)2 = 10 - (QR)2

 

QR = 11/4          (PQ = 23/4)

 

AB = 2{sqrt[(BR)2 - (QR)2]}            

 

(AB)2 = 333/4

 

civonamzuk Jun 26, 2021

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