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Let r be the radius of the circle centered at O.  If PD = 10 and PC = 15, and P is the midpoint of OB, what is r?

 

 May 13, 2020
 #1
avatar+111438 
+1

We can use the intersecting chord theorem here

 

Note that   AO  = r

And OP  = (1/2)r

And PB = (1/2)r

 

So we  have  that

 

PD * PC  =  (AO + OP) (PB)

 

10 * 15  =  [r + (1/2)r ] [ (1/2)r]       simplify

 

150  =  (3/2)r * (1/2)r

 

150  =  (3/4)r^2           multiply both sides by   4/3

 

200  = r^2   take the  positive root

 

√200 = r

 

10√2 =  r

 

 

cool cool cool

 May 13, 2020
edited by CPhill  May 13, 2020
 #2
avatar+1082 
+1

Excellent job, Phill !!!

Dragan  May 13, 2020
 #3
avatar+111438 
0

THX, Dragan  !!!!

 

cool cool cool

CPhill  May 13, 2020

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