A) Isosceles and right angled
B) Isosceles but not right angled
C) Right angled but not isosceles
D) Neither right angled nor isosceles
Correct Answer: A
Solution :
Let \[A\,(4,\,\,0),\,\,B\,(-1,\,-1),\,\,C\,(3,\,\,5)\] then \[AB=\sqrt{26},\] \[AC=\sqrt{26}\] and\[BC=\sqrt{52}\,\,i.e.,\,\,\,AB=AC\]. Hence triangle is isosceles. Also, \[{{(BC)}^{2}}=A{{B}^{2}}+A{{C}^{2}}\] Hence triangle is right angled also.
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