A circle drawn with origin as the centre passes through (13/2, 0). The point which does not lie in the interior of the circle is
a. -¾, 1
b. 2, 7/3
c. 5, -1/2
d. (-6, 5/2)

Solution:

It is given that

A circle is drawn with origin as centre (0, 0) passes through (13/2, 0)

We know that

Radius of the circle = Distance between the two points

\(=\sqrt{(\frac{13}{2}-0)^{2}+(0-0)^{2}}=\sqrt{(\frac{13}{2})^{2}}=\frac{13}{2}=6.5\)

A point lies inside, on or outside the circle if the distance of the point from the centre of the circle is less than, equal to or greater than the radius of the circle.

Let us now check the options one by one

a. The distance between (0, 0) and (-3/4, 1)

\(\\=\sqrt{(\frac{-3}{4}-0)^{2}+(1-0)^{2}} \\ \\=\sqrt{\frac{9}{16}+1} \\ \\=\sqrt{\frac{25}{16}}\)

= 5/4

= 1.25 < 6.5

(-3/4, 1) lies in the interior of the circle.

b. The distance between (0, 0) and (2, 7/3)

\(\\=\sqrt{(2-0)^{2}+(\frac{7}{3}-0)^{2}} \\ \\=\sqrt{4+\frac{49}{9}} \\ \\=\sqrt{\frac{36+49}{9}} \\ \\=\sqrt{\frac{85}{9}}\)

= 9.22/3

= 3.1 < 6.5

(2, 7/3) lies in the interior of the circle.

c. The distance between (0, 0) and (5, -1/2)

\(\\=\sqrt{(5-0)^{2}+(\frac{-1}{2}-0)^{2}} \\ \\=\sqrt{25+\frac{1}{4}} \\ \\=\sqrt{\frac{101}{4}}\)

= 10.04/2

= 5.02 < 6.5

(5, -1/2) lies in the interior of the circle.

d. The distance between (0, 0) and (-6, 5/2)

\(\\=\sqrt{(-6-0)^{2}+(\frac{5}{2}-0)^{2}} \\ \\=\sqrt{36+\frac{25}{4}} \\ \\=\sqrt{\frac{144+25}{4}} \\ \\=\sqrt{\frac{169}{4}}\)

= 13/2

= 6.5

(-6, 5/2) lies on the circle.

Therefore, the point (-6, 5/2) does not lie in the interior of the circle.

✦ Try This: The perpendicular bisector of the line segment joining the points R (5, 6) and S (7, 8) cuts the y-axis at

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

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NCERT Exemplar Class 10 Maths Exercise 7.1 Problem 16

A circle drawn with origin as the centre passes through (13/2, 0). The point which does not lie in the interior of the circle is a. -¾, 1, b. 2, 7/3, c. 5, -1/2, d. (-6, 5/2)

Summary:

A circle drawn with origin as the centre passes through (13/2, 0). The point which does not lie in the interior of the circle is (-6, 5/2)

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