A diameter and similar right triangles

A diameter and similar right triangles

Secondary 2
8 marks
TGM Original Questions

Core stretch

\(AC\) is a diameter of a circle with centre \(D\) and radius 6 cm. Point \(B\) lies on the circle, \(E\) lies on \(BC\), \(DE=4.5\) cm, and \(DE\perp AC\). Also \(\angle ABC=90^\circ\). Find

The triangles \(ABC\) and \(EDC\) are given to be similar.

  1. \(\angle ACB\) to 1 decimal place,[2]
  2. \(AB\) to 3 significant figures,[2]
  3. one pair of similar triangles,[2]
  4. \(AB/BC\).[2]

Give non-exact lengths and areas to 3 significant figures, and angles to 1 decimal place.

Solution:

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Answer:(a) \(36.9^\circ\) (b) \(7.20\) cm (c) \(\triangle ABC\sim\triangle EDC\) (d) \(3/4\).

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