Option C:
The length of SP is 12.
Solution:
In the given circle, NP and MQ are chords of the circle.
MS = 3, NS = 2, SQ = 8
To find the length of SP:
Segments of chords theorem:
If two chords intersects in the interior of a circle, then the product of the lengths of the segment of one chord is equal to the product of lengths of the segments of the other chord.
By this theorem,
NS × SP = MS × SQ
⇒ 2 × SP = 3 × 8
⇒ 2 SP = 24
Divide by 2 on both sides of the equation, we get
⇒ SP = 12
Option C is the correct answer.
The length of SP is 12.