TS EAMCET · Maths · Three Dimensional Geometry
\(A(2,3, k), B(-1, k,-1), C(4,-3,2)\) are the vertices of \(\triangle A B C\). If \(A B=A C\) and \(k\gt0\), then \(A B C\) is
- A an equilateral triangle
- B a right-angled isosceles triangle
- C an isosceles triangle but not right angled
- D an obtuse angled isosceles triangle
Answer & Solution
Correct Answer
(B) a right-angled isosceles triangle
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Given that } A B=A C \\ & \therefore 9+(3-k)^2+(k+1)^2=4+36+(2-k)^2 \\ & \Rightarrow k^2=25 \Rightarrow k=5 \quad(\because k\gt0)\end{aligned}\) \(\therefore A B=A C=\sqrt{9+4+36}=7 ; B C=\sqrt{25+64+9}=\sqrt{98}\) \(\because A B^2+A C^2=B C^2\) and…
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