Chords NP and MQ intersect at point S in circle R.
If MS = 3, NS = 2, and SQ = 8, what is the length of SP?

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.

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363