SOLUTION: segment AB, which is 25 inches long, is the diameter of a circle. chord PQ meets AB perpendicularly at C, where AC = 16 inches. find the length of PQ.

Algebra ->  Circles -> SOLUTION: segment AB, which is 25 inches long, is the diameter of a circle. chord PQ meets AB perpendicularly at C, where AC = 16 inches. find the length of PQ.       Log On


   

Question 626521: segment AB, which is 25 inches long, is the diameter of a circle. chord PQ meets AB perpendicularly at C, where AC = 16 inches. find the length of PQ.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Since AB=25 and AC=16, then BC = AB-AC = 25-16 = 9



Draw in AP and BP



∠APB is a right angle because it is inscribed in a semicircle.

The three right triangles ᐃAPB, ᐃACP and ᐃPCB are all similar 
because their corresponding angles are equal.  Therefore 

AC%2FPC = PC%2FBC

16%2FPC = PC%2F9

Cross-multiplying:

PC˛ = 144
 PC = 12

By symmetry, PC = QC, so PQ = 12ˇ2 = 24.

Edwin