Mathematics
Three isosceles triangles PBC, QBC and RBC are on the same base, then :
P, Q and R are collinear.
△PQR is isosceles triangle.
Q lies on the circumference of a circle with BC as diameter.
Q is mid-point of line segment PR.
Locus
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Answer
Steps of construction :
Draw a line segment BC.
Draw XY, perpendicular bisector of BC.
We know that,
Locus of a point equidistant from two given points is the perpendicular bisector of the line joining the two points.
Thus, any point on the line XY is at equal distance from B and C.
∴ P, Q and R lies on the line XY.
Hence, Option 1 is the correct option.
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Related Questions
A straight line AB is 8 cm long. Draw and describe the locus of a point which is :
(i) always 4 cm from the line AB.
(ii) equidistant from A and B.
Mark the two points X and Y, which are 4 cm from AB and equidistant from A and B. Describe the figure AXBY.
The locus of point which is equidistant from two non-parallel lines AB and CD is :
perpendicular to AB.
perpendicular to CD.
bisector of angle between AB and CD.
perpendicular bisector of CD.
Locus of the centers of the circles passing through two fixed points A and B is :
a line parallel to line segment AB.
the bisector of the line segment AB.
perpendicular to line segment AB.
perpendicular bisector of line segment AB.
A point is equidistant from the sides of an obtuse angle triangle. The point is called :
circumcenter of the triangle.
incenter of the triangle.
centroid of the triangle.
orthocenter of the triangle.