Question

IN A RIGHT ANGLE ISOSELES TRIANGLE ABC RIGHT ANGLED AT B,BP IS PERPENDICULAR TO AC.PROVE THAT AP =BP×AC.(IRRELEVENT ANSWER WOULD BE REPORTED)​

Answer 1

Step-by-step explanation:

How will I prove this? In a right isosceles triangle, △ABC, right angled at B,BP is perpendicular to AC. Prove that AP=BP×AC.

I presume that point P lies on AC.

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

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

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

⇒AP=PC=12AC=12√AB.

⇒BP=12√AB since △ABP is right angled.

Thus we get, LHS=AP=12√AB, and,

RHS=BP×AC=12√AB×2–√AB=AB2≠LHS.

Hope it helps you mate :)