Multiple choice

From the circumcentre L of △XYZ, perpendicular LM is drawn on side YZ. If ∠YXZ=60∘, then the measure of ∠YLM is:

  1. 60∘

  2. 120∘

  3. 180∘

  4. 90∘
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A Correct answer
Explanation

Since L is the circumcentre, it's equidistant from all vertices. LM is the perpendicular bisector of YZ, so LY = LZ and triangles LYM and LZM are congruent right triangles. Angle YLZ (central angle) = 2 × angle YXZ = 2 × 60° = 120°. Therefore angle YLM = 120°/2 = 60°. 120° is the full central angle, 90° would be for orthocentre properties, and 180° is a straight angle.

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