MathematicsABC is a right angled triangle , with C = 90∘. If P is the perpendicular from C to AB and a,b,c have the usual meaning, then find the value of 1a2+1b2.

ABC is a right angled triangle , with C = 90. If P is the perpendicular from C to AB and a,b,c have the usual meaning, then find the value of 1a2+1b2.


  1. A
    p2
  2. B
    1p2
  3. C
    p
  4. D
    1p 

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    Solution:

    Given ABC is a right-angled triangle with the right angle at C.
    Let P is the perpendicular from C to AB and it intersects AB at D . Given, the length of the side AB = c, BC = a, CA = b and CD = p .
    Area of triangle ABC = 12×BC×AC=12ab
    Also, Area of triangle ABC = 12×AB×CD=12cp
    ab=cp
    Since a2+b2=c2=abp2=a2b2p2
    1a2+1b2=1p2
      
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