Question

In the diagram, QN:NP = 2:3 and QP=10. Find the radius of circle O.

Answer 1

√253

Explanation:

Extend the lines to the circumference of the circle as shown in my diagram. If QN:NP = 2:3, then QN = 2/5(10) = 4, and NP = 10 - 4 = 6.

Then we use the intersecting secants theorem to find the length ST: 4(10) = 2(14 + ST)

After some rearranging we get ST = 6 (ignore the 4 in the diagram sorry).

Finally we use the intersecting chords theorem to find the radius, r: (r - 13)(r + 13) = 14(6)

Using difference of 2 squares on the left we get r² -169 = 84

So r = √253