NECO 2023 · Paper 1 · Q43

In the diagram, KTNKTN is a tangent to the circle at TT and ∠ABT=65∘\angle ABT = 65^\circ. Find ∠NTA\angle NTA.

65°TABKN
Worked solution (try it first)
  1. ∠NTA\angle NTA is between the tangent TNTN and the chord TATA.
  2. The angle between a tangent and a chord equals the angle in the alternate segment, here ∠ABT\angle ABT.
  3. So ∠NTA=65∘\angle NTA = 65^\circ, option C.

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