Multiple choice

Quadrilateral ABCD is inscribed in a circle with radius $1$ unit AC is the diameter of the circle and $BD=AB$. The diagonal cut at P. If $PC=\dfrac{2}{5}$ then the length of CD is equal to

  1. $\dfrac{2}{3}$
  2. $\dfrac{2}{7}$
  3. $\dfrac{1}{8}$
  4. $\dfrac{3}{4}$
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A Correct answer
Explanation

Since AC is diameter, angle ABC = 90 degrees. In triangle ABC, BD=AB, so triangle ABD is isosceles. Using geometric properties of chords and segments in a circle, the segments satisfy power of a point or similar triangles. Given PC=2/5 and radius=1, the calculation leads to CD=2/3.

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