In ΔABC AD⊥BC and AD²=BD.DC. The measure of ∠BAC is:

  1. 90o
  2. 45o
  3. 60o
  4. 75o
Monis Rasool Professor Asked on 21st November 2015 in Maths.
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  • 1 Answer(s)

    Correct option is (1) 90° 

    Explanation:-
    In Δ ABC,

    RE: In ΔABC AD⊥BC and AD²=BD.DC. The measure of ∠BAC is:


    AD⊥ BC  and  AD² = BD. DC               (Given in the question)
    In Δ ADB,
    AB² + AD² + BD²       ……………………. (1)
    In Δ ACD,
    AC² = AD² + CD²

    Add equation (1) and (2),
    AB² + AC² = AD² + AD² + BD² + CD²
    AB² + AC² = 2. AD² + BD² + CD²
    AB² + AC² = 2. BD. CD + BD² + CD²              {AD² = BD. DC (Given)}
    = (BD + CD)²                             {(a + b)² = a² + b² + 2ab}
    AB² + AC² = BC²
    So, Δ ABC is a right triangle and right triangle at A.
    Then, the ∠BAC = 90°

    Hence, the answer is (1) 90°.

    Monis Rasool Professor Answered on 21st November 2015.
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