Question

IN A RIGHT ANGLE ISOSELES TRIANGLE ABC RIGHT ANGLED AT B,BP IS PERPENDICULAR TO AC.PROVE THAT AP =BP×AC.

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Answer 1

  Ipresume that point PP lies on AC.AC.

You cannot prove it because what is sought to be proved is wrong.

Since △ABC△ABC is an isosceles right angled triangle, AC=2–√AB.AC=2AB.

It can easily be shown that △ABP≅△CBP.△ABP≅△CBP.

⇒AP=PC=12AC=12√AB.⇒AP=PC=12AC=12AB.

⇒BP=12√AB⇒BP=12AB since △ABP△ABP is right angled.

Thus we get, LHS=AP=12√AB,LHS=AP=12AB, and,

RHS=BP×AC=12√AB×2–√AB=AB2≠LHS.

hope it helps you