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JAMB 2002 · UME · Q10

In the diagram, XZXZ is the diameter of the circle XYZXYZ with centre OO and radius 152\frac{15}{2} cm. If XY=12XY = 12 cm, find the area of the triangle XYZXYZ.

OXZY
Worked solution (try it first)
  1. XZXZ is a diameter, so ∠XYZ=90∘\angle XYZ = 90^\circ (angle in a semicircle).
  2. The diameter is 2×152=152 \times \frac{15}{2} = 15 cm.
  3. Pythagoras: YZ2=152−122=81YZ^2 = 15^2 - 12^2 = 81, so YZ=9YZ = 9 cm.
  4. The two sides at the right angle are the base and height: area =12×12×9= \frac12 \times 12 \times 9
    =54 cm2= 54\text{ cm}^2, option B.

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