# Statement 1: The lines  and  form an isosceles triangle Statement 2: If internal bisector of any of triangle is perpendicular to the opposite side, then the given triangle is isosceles a) Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1 b) Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1 c) Statement 1 is True, Statement 2 is False d) Statement 1 is False, Statement 2 is True

## Question ID - 54542 :- Statement 1: The lines  and  form an isosceles triangle Statement 2: If internal bisector of any of triangle is perpendicular to the opposite side, then the given triangle is isosceles a) Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1 b) Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1 c) Statement 1 is True, Statement 2 is False d) Statement 1 is False, Statement 2 is True

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(a)

The given lines are

(i)

(ii)

(iii)

The triangle formed by the lines (i), (ii) and (iii) is an isosceles triangle if the internal bisector of the vertical angle is perpendicular to the third side. Now equations of bisectors of the angle between lines (i) and (ii) are

or    (iv)

and     (v)

Obviously the bisector (iv) is perpendicular to the third side of the triangle. Hence, the given lines form an isosceles triangle

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 Statement 1: If the vertices of a triangle are having rational coordinates then its centroid, circumcentre and orthocentre are rational Statement 2: In any triangle, orthocentre, centroid and circumcentre are collinear and centroid divides the line joining orthocentre and circumcentre in the ratio 2:1 a) Statement 1 is True, Statement 2 is True; Statement 2 is correct explanation for Statement 1 b) Statement 1 is True, Statement 2 is True; Statement 2 is not correct explanation for Statement 1 c) Statement 1 is True, Statement 2 is False d) Statement 1 is False, Statement 2 is True