A right triangle PQR, has its hypotenuse, PR, trisected at points A and B. Two lines, QA and QB are then drawn and k is such that QA^2 + QB^2 = (PR^2) * k. Find the value of k.
DRAW THE TRIANGLE FIRST and observe AP=AB=BR plus
PQ^2 + QR^2 = PR^2
in triangle PQB , QA is median so
2(QA^2 + AP^2) = PQ^2 + QB ^2 (Apollonius theorem)
Similarly in triangle AQR
2(QB^2 + AB^2)=QA^2 + QR^2 (Apollonius theorem)
ADD em nd get the result
QB^2 + QA^2 = 5/9 PR^2

Posted by phi
on 20060309 05:22:58 