Assertion -consider - ABC whose verticies are A - 3 - 4 cos - - - 5 - 4 sin - B - 3 - 4 cos - - 2-3 -5 - 4sin - - 2-3 C - 3 - 4 cos - - 4-3 -5 - 4sin - - 4-3 The orthocentre of the triangle is 3- 5 Reason- consider - ABC whose verticies are A - 3 - 4 cos - - - 5 - 4 sin - B - 3 - 4 cos - - 2-3 -5 - 4sin - - 2-3 C - 3 - 4 cos - - 4-3 -5 - 4sin - - 4-3 The triangle ABC is equilateral

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Integration by Partial Fractions

Assertion :co...

Question

Assertion :consider $Δ$ ABC whose verticies are A = (3 + 4 cos $Θ, - 5 + 4 s i n Θ$ )
$B = (3 + 4 c o s (Θ + \frac{2 π}{3}), - 5 + 4 s i n (Θ + \frac{2 π}{3}))$
$C = (3 + 4 c o s (Θ + \frac{4 π}{3}), - 5 + 4 s i n (Θ + \frac{4 π}{3}))$
The orthocentre of the triangle is (3, 5) Reason: consider $Δ$ ABC whose verticies are A = (3 + 4 cos $Θ, - 5 + 4 s i n Θ$ )
$B = (3 + 4 c o s (Θ + \frac{2 π}{3}), - 5 + 4 s i n (Θ + \frac{2 π}{3}))$
$C = (3 + 4 c o s (Θ + \frac{4 π}{3}), - 5 + 4 s i n (Θ + \frac{4 π}{3}))$
The triangle ABC is equilateral

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$Δ$ is equilateral and its circumcentre is (3, 5) and circumradius is 4.

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Similar questions

Q. Assertion :

{cos}^{3} α + {cos}^{3} (α + \frac{2 π}{3}) + {cos}^{3} (α + \frac{4 π}{3}) = 3 cos α cos (α + \frac{2 π}{3}) cos (α + \frac{4 π}{3})

Reason: If

a + b + c = 0 \Leftrightarrow a^{3} + b^{3} + c^{3} = 3 a b c

Q. Assertion :

{sin}^{3} x + {sin}^{3} (x + \frac{2 π}{3}) + {sin}^{3} (x + \frac{4 π}{3}) = 3 sin x sin (x + \frac{2 π}{3}) \cdot sin (x + \frac{4 π}{3})

Reason: If

a + b + c = 0

, then

a^{3} + b^{3} + c^{3} = 3 a b c

Q. Assertion: The value of (25)³ + (−16)³ + (−9)³ is 10800.
Reason: If a + b + c = 0, then a³ + b³ + c³ = 3abc.

(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true and but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Assertion: Area of the triangle whose
vertices are $A (\frac{- 3}{2}, 3), B (6, - 2)$ and $C (- 3, 4)$ is 0
Reason : The points A, B and C are collinear

Assertion: The sides of a triangle are 3cm, 4cm and 5cm. Its area is $6 c m^{2}$

Reason: If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area

$= \sqrt{(s - a) (s - b) (s - c)}$

Which of the following is correct?

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The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionΔ is equilateral and its circumcentre is (3, 5) and circumradius is 4.

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
$Δ$ is equilateral and its circumcentre is (3, 5) and circumradius is 4.