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jai kohli
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Asked: 2023-02-15T07:19:09+00:00 In:

ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that AC²= AB² + BC² + 2 BC . BD.

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How to Pythagorean theorem is a fundamental concept in geometry.
How to use the Pythagorean theorem.
Triangles Solutions for Class 10th Maths, EXERCISE 6.6, Questions No:2
CBSE Board and Others state Board.

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      ABC is a triangle in which ∠ABC > 90° and AD ⊥ CB produced. Prove that AC²= AB² + BC² + 2 BC . BD.

      In ΔADB, by pythagoras theorem
      AB² = AD² + DB² …(1)
      In ΔACD, by pythagoras theorem
      AC² = AD² + DC²
      ⇒AC² = AD² + (DB + BC)²
      ⇒AC² = AD² + BD² + BC² + 2DB BC
      ⇒AC² = AB² + BC² + 2DB × BC [From the equation (1)]

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