Explanation:

AB = CD = 10 cm, PB = 3 cm; AP = (10-3) = 7 cm, OC = 13 cm

Extending line MN, such that it is the diameter of the circle.

Since MN is the diameter; MN = 2OC = 2*13 = 26 cm

As per theorem of chords intersecting each other in a circle: AP*PB = MP*PN

=> 7*3 = (MN – PN) *PN

=> 21 = (26 – PN) * PN => PN² – 26 PN + 21 = 0

Applying formula,

PN = {-(-26) (+/-) √(-26)2 + (4*21)} / 2

(Discarding the negative root) PN = 13 + 2√37 or 13 - 2√37

Now, OP = ON – PN = 13 – (13 + 2√37) or 13 – (13 - 2√37)

Since the first case will yield a negative value, so we will discard it. Thus, OP = 2√37