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Coordinate Geometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
Question
State whether the following statements are true or false. Justify your answer.
A circle has its centre at the origin and a point P(5, 0) lies on it. The point Q(6, 8) lies outside the circle.
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Answer

True:If the distance of $Q$ from the cente $O(0,0)$ is greater than the radius then point $Q$ lies in the exterior of the circle. Point $P(5,0)$ lies on thr circle and centre is at $O(0,0)$ so radius $=O P$
$\Rightarrow O P^2=\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2$
$\Rightarrow O P^2=(5-0)^2+(0-0)^2$
$\Rightarrow O P^2=5^2$
$\Rightarrow O P=5 \text { units }$
Now, $O Q^2=(6-0)^2+(8-0)^2$
$\Rightarrow O Q^2=36+64$
$\Rightarrow O Q^2=100$
$\Rightarrow O Q=10 \text { units }$
$\Rightarrow O Q>O P \text { (radius) }$
So, point Q lies exterior to circle.

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