Explanation:
Your answers for 1 and 2 are correct. MN and LN are both radii of the circle, and therefore equal. And NK can be found using Pythagorean theorem.
To find LP (and PM), we can use similar triangles:
LN / NK = LP / LK
10 / 26 = LP / 24
LP ≈ 9.23
PM ≈ 9.23
LM ≈ 2 × 9.23 = 18.46
To find NP, we can again use similar triangles.
NP / NL = NL / NK
NP / 10 = 10 / 26
NP ≈ 3.85
NQ is a radius of the circle, so it is equal to 10. PQ is therefore:
PQ ≈ 10 − 3.85 = 6.15
As you found, QK = 26 − 10 = 16.
Before we find LR, let's find RK using similar triangles.
RK / QK = NK / LK
RK / 16 = 26 / 24
RK ≈ 17.33
LR ≈ 24 − 17.33 = 6.67
As you found, MK = 24.
And finally, MS = LR ≈ 6.67.