+0  
 
0
39
1
avatar

Let AB and CD be chords of a circle, that meet at point Q inside the circle. If AQ = 6, BQ = 12, and CD = 30, then find the minimum length of CQ.

 Feb 8, 2021
 #1
avatar+8456 
0

Let x be the length of CQ. Then DQ = 30 - x.

 

By power of points,

 

x(30 - x) = 72

x^2 - 30x + 72 = 0

(x - 15)^2 - 225 + 72 = 0

(x - 15)^2 = 153

\(x = 15\pm \sqrt{153}\)

 

Minimum length of CQ = \(15 - \sqrt{153}\)

 Feb 8, 2021

92 Online Users

avatar
avatar
avatar
avatar