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Chord Properties of Circles

When a circle...

Question

When a circle and a line are in a plane, they will always have only two points of intersection.

A

True

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B

False

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Solution

The correct option is B False

When a circle and a line lie in a plane, they can have either 0, 1 or 2 points of intersection, as shown in the given figure.The line which touches the circle at only one point is called the tangent of the circle.The line which touches the circle at two points is called the secant of the circle.

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Similar questions

Q. When a circle and a line are in a plane, they may have ____ point/points of intersection.

Q. Which of the following statements are true?
(i) A line segment has no definite length.
(ii) A ray has no end-point.
(iii) A line has a definite length.
(iv) A line

\overset{\leftrightarrow}{A B}

is same as line

\overset{\leftrightarrow}{B A}

\underset{A B}{\to}

\underset{B A}{\to}

.
(vi) Two distinct points always determine a unique line.
(vii) Three lines are concurrent if they have a common point.
(viii) Two distinct lines cannot have more than one point in common.
(ix) Two intersecting lines cannot be both parallel to the same line.
(x) Open half-line OA is same as ray

\underset{O A}{\to}

.
(xi) Two lines may intersect at two points.
(xii) Two lines l and m are parallel only when they have no point in common.

Q. Write the turth value (T/F) of each of the following statements:

(i) Two lines intersect in a point.

(ii) Two lines may intersect in two points.

(iii) A segment has no length.

(iv) Two distinct points always determine a line.

(v) Every ray has a finite length.

(vi) A ray has one end-point only.

(vii) A segment has one end-point only.

(viii) The ray AB is same as ray BA.

(ix) Only a single line may pass through a given point.

(x) Two lines are coincident if they have only one point in common.

Q. State which of the following statements are true (T) and which are false (F).

(i) Point has a size because we can see it as a thick dot on paper.
(ii) By liens in geometry, we mean only straight lines.
(iii) Two lines in a plane always intersect in a point.
(iv) Any plane through a vertical line is vertical.
(v) Any plane through a horizontal line is horizontal.
(vi) There cannot be a horizontal line a vertical plane.
(vii) All lines in a horizontal plane are horizontal.
(viii) Two lines in a plane always intersect in a point.
(ix) If two lines intersect at a point P, then P is called the point of concurrence of the two lines.
(x) If two lines intersect at a point P, then p is called the point of intersection of the two lines.
(xi) If A,B,C and D are collinear points D, P and Q are collinear, then points A, B, C, D, P and Q are always collinear.
(xii) Two different lines can be drawn passing through two given points.
(xiii) Through a given point only one line can be drawn.
(xiv) Four points are collinear if any three of them lie on the same line.
(xv) The maximum number of points of intersection of three lines is three.
(xvi) The minimum number of points of intersection of three lines is one.

___ is a line that intersects a circle at only one point, and ___ is a line that intersects a circle at two distinct points.

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