We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
69
2
avatar

Point O is the circumcenter of triangle ABC. The distance between O and Line AC is 7, and the distance between  O  and  Line AB is 15. If AC=48, what is AB?

 Nov 9, 2019
 #2
avatar+104933 
+1

OD   = 7

 

Since O  is the circumcenter, OD  is a perpendicular bisector  of  AC

 

So  DA  = (1/2) 48  = 24

 

And  OA  = sqrt ( OD^2  +  DA^2)   =  sqrt (7^2 + 24^2)  = sqrt (625)   =  25 

 

So triangle  OAD   is a  7 - 24 - 25  right triangle

 

And OE  =  15    and is also a perpendicular bisector of side AB

 

So triangle OAE  is a right triangle

 

And  EA  = sqrt  ( OA^2  - OE^2)  =  sqrt  ( 25^2  - 15^2)  =  sqrt (400)  =  20

 

And AB  is twice EA  =   40

 

 

cool cool cool

 Nov 9, 2019

31 Online Users

avatar
avatar