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The figures shows a circle of diameter AB and radius $6.5$ cm. If chord CA is $5$ cm long, find the area of triangle ABC.

  1. $60$ sq.cm.
  2. $30$ sq.cm
  3. $40$ sq.cm.
  4. $52$ sq.cm.

 

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1 Answer

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In the triangle ABC , Angle ACB = 90 degree (Angle Subtended by the Diameter = 90 degree)

AC = 5cm

AB = 6.5 * 2 = 13 cm

using Pythagoras theorem

$AB^{2} = AC^{2} + CB^{2}$

$CB = \sqrt{13^{2} - 5^{2}}$ = 12

Area of triangle ABC = 0.5 * AC * CB = 30 sq.cm.

Option B is the Correct Answer.

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