Question

ABC is a right triangle, right angled at B. If P is the length of the perpendicular from B to AC and AB c  , BC a  and CA b  , then prove that (a) 2 2 2 1 1 1 p a c  

Answer 1

Answer:

Here, ABC is a right triangle,

In which ∠C = 90°, AB =c, AC= b, BC = a,

Also, p is the length of the perpendicular from c to ab,

We have to prove that:

Proof:

Let D be the point on the segment AB,

Such that CD = p,

In triangle ACB and ADC,

   ( reflexive )

  ( Right angle )

By AA similarity postulate,

By the property of similar triangles,

------------ (1)

Now, by the Pythagoras theorem,

Hence, proved