Mathematics 10 — Exercise 9.2 · Q4

Full question

AC is a diameter, AB=AD, and EF is tangent at C. Angle BCE=70°. Find x=ACD.

OABCDEFAB=AD; ∠BCE=70°x=ACDDiagram not to scale

Step-by-step solution

  1. AC is perpendicular to CE, so BCA=90°−70°=20°.

  2. Equal chords AB and AD subtend equal angles at C. Thus ACD=BCA.

  3. Substitute the given numbers into the formula.

    90−70

  4. Calculate this operation before combining the remaining terms.

    90−70=20

  5. The required result is shown below. Unit: °

    20

Answer

The final answer is shown below.

20