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STD 11 - rectangular cartensian co-ordinates — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - rectangular cartensian co-ordinates4 Marks
MCQ
Let $P$ be a point inside a $\triangle A B C$ with $\angle A B C=90^{\circ}$. Let $P_1$ and $P_2$ be the images of $P$ under reflection in $A B$ and $B C$ respectively. The distance between the circumcenters of $\triangle A B C$ and $P_1 P P_2$ is
  • A
    $\frac{A B}{2}$
  • B
    $\frac{A P+B P+C P}{3}$
  • ✓
    $\frac{A C}{2}$
  • D
    $\frac{A B+B C+A C}{2}$
✓

Answer

Correct option: C.
$\frac{A C}{2}$
c
(c)

$A B C$ is a right angled triangle, $\angle A B C=90^{\circ}$

Circumcentre of $\triangle A B C$ is mid-point of $A C$ i.e. $M$.

Circumcentre of $\Delta P_1 P P_2$ is mid-point of $P_1 P_2$

$A B$ is perpendicular bisector of $P P_1$ and $B C$ is perpendicular bisector of $P P_2$.

Perpendicular bisector of $P P_1$ and $P P_2$ intersect at $B$.

$\therefore B$ is circumcentre of $\Delta P_1 P P_2$.

$\therefore$ Distance between

$B M=A M=M C=\frac{A C}{2}$

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