SOLUTION: Given circle T; and a point P outside of T;, 2 lines l1 and l2 are drawn such that both pass through P. l1 intersects T; at A and B, and l2 intersects T; at C and D, with C between

Algebra ->  Circles -> SOLUTION: Given circle T; and a point P outside of T;, 2 lines l1 and l2 are drawn such that both pass through P. l1 intersects T; at A and B, and l2 intersects T; at C and D, with C between      Log On


   

Question 697522: Given circle T; and a point P outside of T;, 2 lines l1 and l2 are drawn such that both pass through P. l1 intersects T; at A and B, and l2 intersects T; at C and D, with C between D and P. If PA=44,PB=294 and PC=56, what is PD?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
PA=44,PB=294 and PC=56, what is PD?

 
Draw BC and AD

 

Angles B and D are inscribed angles intersepting
the same arc AC so they are equal.
Angle P is in both triangles. Therefore triangles 
PAD and PCB are similar, therefore

PA%2F%28PC%29 = PD%2F%28PB%29

Cross-multiplying:

PA×PB = PC×PD

44×294 = 56×PD

12936 = 56×PD

12936%2F56 = PD

231 = PD

So PD = 231

Edwin