<p><strong>Let A(, 2), B(, 6) and <math><mrow><mi>C</mi><mrow><mo>(</mo><mrow><mfrac><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></mfrac><mo>,</mo><mo>−</mo><mn>2</mn></mrow><mo>)</mo></mrow></mrow></math> be vertices of a <math><mrow><mi>Δ</mi><mi>A</mi><mi>B</mi><mi>C</mi><mo>.</mo></mrow></math> If <math><mrow><mrow><mo>(</mo><mrow><mn>5</mn><mo>,</mo><mfrac><mrow><mi>α</mi></mrow><mrow><mn>4</mn></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math> is the circumcentre of <math><mrow><mi>Δ</mi><mi>A</mi><mi>B</mi><mi>C</mi><mo>,</mo></mrow></math> then which of the following is NOT correct about <math><mrow><mi>Δ</mi><mi>A</mi><mi>B</mi><mi>C</mi><mo>?</mo></mrow></math></strong></p>

Circumcentre (D) ≡ (5, α4) (5−α)2+ (α4+2)2= (5−α)2+ (α4−6)2............... (i) (5−α4)2+ (α4+2)2.................... (ii) (i) α4+2=± (α4−6) (ii) 9 + 16 = 9 + 16⊕→x (−)→α2=4⇒α=8ar (ABC)=242S = 24R = 5, r = Δs=2412=2

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Straight Lines Ncert Solutions Maths class 11th Maths Class 11th

Let A(, 2), B(, 6) and $C (\frac{α}{4}, - 2)$ be vertices of a $Δ A B C .$ If $(5, \frac{α}{4})$ is the circumcentre of $Δ A B C,$ then which of the following is NOT correct about $Δ A B C ?$

Option 1 -

area is 24

Option 2 -

perimeter is 25

Option 3 -

circumradius is 5

Option 4 -

inradius is 2

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1 Answer

Answered by

Payal Gupta | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

Circumcentre (D) $\equiv (5, \frac{α}{4})$

${(5 - α)}^{2} + {(\frac{α}{4} + 2)}^{2} = {(5 - α)}^{2} + {(\frac{α}{4} - 6)}^{2} . . . . . . . . . . . . . . . (i)$

${(5 - \frac{α}{4})}^{2} + {(\frac{α}{4} + 2)}^{2} . . . . . . . . . . . . . . . . . . . . (i i)$

(i) $\frac{α}{4} + 2 = \pm (\frac{α}{4} - 6)$

(ii) 9 + 16 = 9 + 16

$\oplus \to x$

$(-) \to \frac{α}{2} = 4 \Rightarrow α = 8$

ar $(A B C) = 24$

2S = 24

R = 5, r = $\frac{Δ}{s} = \frac{24}{12} = 2$

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Let A(, 2), B(, 6) and $C (\frac{α}{4}, - 2)$ be vertices of a $Δ A B C .$ If $(5, \frac{α}{4})$ is the circumcentre of $Δ A B C,$ then which of the following is NOT correct about $Δ A B C ?$

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Let A(, 2), B(, 6) and C(α4,−2) be vertices of a ΔABC. If (5,α4) is the circumcentre of ΔABC, then which of the following is NOT correct about ΔABC?

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Let A(, 2), B(, 6) and $C (\frac{α}{4}, - 2)$ be vertices of a $Δ A B C .$ If $(5, \frac{α}{4})$ is the circumcentre of $Δ A B C,$ then which of the following is NOT correct about $Δ A B C ?$