X is a point 7cm from the center of circle O with radius 9 cm. AXB is a chord of the circle such that AX= 2 XB. Find the length of AB.

Answer 1

For the chord AB
k=mXB
2k=mAX

We will construct diameter CD such that X lies on CD.
Now CX=9+7=16 cm, XD=9-7=2 cm

Using the theorem of intersecting chords (AB and CD), we have
16*2=k(2k)
Solve for k.