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AP EAMCET202023 Sep 2020Morning ShiftMathematicsProperties of TrianglesActual

ln a △ A B C , A = 30 ° + C and R = ( 3 + 1 ) r , where r is the inradius and R is the circumradius, then

Options

  1. AA B C is a right-angled triangle
  2. BA B C is an equilateral triangle
  3. CA B C is acute angled
  4. D∠ A = 75 ° ,   ∠ B = 60 ° ,   ∠ C = 45 °

Correct answer

A. A B C is a right-angled triangle

Step-by-step solution

Using r = 4 R sin A 2 · sin B 2 · sin C 2 ⇒ R 3 + 1 = 4 R sin A 2 · sin B 2 · sin C 2 ∵ R = 3 + 1 r ⇒ 3 - 1 8 = sin A 2 · sin B 2 · sin C 2 ⇒ sin A 2 · sin B 2 · sin C 2 = 3 - 1 2 2 · 1 2 · 1 2 Now, A 2 ,   B 2 ,   C 2 are 1 2 ,   1 2 ,   3 - 1 2 2 and it is given that A = 30 ° + C So, we can say that A ,   B   &   C are 60 ° ,   90 °   &   30 ° respectively

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