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TS EAMCET · Maths · Properties of Triangles

A triangle ABC has area of P square units and circumference 2S units. If h1, h2 and h3 are respectively the length of the altitudes of the triangle drawn from the vertices A, B and C, then P2h1h2+h2h3+h3h12h12h22h32-2=

  1. A S2-2P2
  2. B cot2A+cot2B+cot2C2
  3. C a+b+c4S
  4. D S2-ab2+bc2+ca2
Verified Solution

Answer & Solution

Correct Answer

(A) S2-2P2

Step-by-step Solution

Detailed explanation

Let, the sides of the triangle ABC are a, b, c units and the corresponding heights are h1, h2, h3 units respectively. Then the circumference is a+b+c=2S and area is P=12ah1=12bh2=12ch3 ⇒h1=2Pa, h2=2Pb, h3=2Pc. Now P2h1h2+h2h3+h3h12h12h22h32-2…