sidtheslothisbae sidtheslothisbae
  • 24-04-2022
  • Mathematics
contestada

given: tangent TA is parallel to KM. Prove: KS = MS

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topeadeniran2 topeadeniran2
  • 02-05-2022

When tangent TA is parallel to KM, it can be proved that KS = MS since they're congruent.

How to prove the tangent?

It should be noted that when the tangent line TA is parallel to chord KM, it simply means that segment KS and MS are congruent.

Therefore, since they're congruent, SKM and SMK are equal. By the theorem of inscribed angle, we will have:

SKM = 1/2m(MS)

SKM = 1/2m(KS).

Since SKM = SMK

1/2m(MS) = 1/2m(KS).

MS = KS

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