Maths-
General
Easy

Question

In-circle of radius 4 cm of a triangle ABC touches the side BC at D. If BD = 6cm., DC = 8 cm, then the area of the triangle ABC is-

  1. 42 cm squared
  2. 84 cm squared
  3. 84 over 3 cm squared
  4. None of these

The correct answer is: 84 cm squared


    We have straight angle IBD equals straight B over 2 straight angle ICD equals straight C over 2

    B D equals 6 cm comma C D equals 8 cm not stretchy rightwards double arrow B C equals a equals 14 cm. text  Also,  end text I D equals r equals 4 cm
    Now, tan invisible function application straight B over 2 equals 4 over 6 equals 2 over 3 text  and  end text tan invisible function application straight C over 2 equals 4 over 8 equals 1 half
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell tan invisible function application straight B over 2 tan invisible function application straight C over 2 equals square root of fraction numerator left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight c right parenthesis over denominator straight s left parenthesis straight s minus straight b right parenthesis end fraction end root end cell row cell cross times square root of fraction numerator left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis over denominator straight s left parenthesis straight s minus straight c right parenthesis end fraction end root equals fraction numerator straight s minus straight a over denominator straight s end fraction end cell row cell therefore 2 over 3 cross times 1 half equals fraction numerator straight s minus 14 over denominator straight s end fraction not stretchy rightwards double arrow straight s equals 21 cm end cell end table
    therefore text  Area,  end text straight capital delta equals rs equals 4 cross times 21 equals 84 cm squared

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