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KVPY2016MathematicsProperties of Triangles

Consider a semicircle of radius 1 unit constructed on the diameter AB , and let O be its centre. Let C be a point on AO such that AC : CO =2: 1 . Draw CD perpendicular to AO with D on the semicircle. Draw OE perpendicular to AD with E on AD. Let OE and CD intersects at H . Then DH equals

Options

  1. A1 5
  2. B1 3
  3. C1 2
  4. D5 -1 2

Correct answer

C. 1 2

Step-by-step solution

'E' is mid point of A D . array l 2 = 1 3 2 ² -1= 1 3 ² = 2 3 = 2 3 = 1- 2 3 = 1 3 array ED 1 = 1 3 DH = ED = 1 3 3 2 = 1 2

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