AB is a line segment in a plane. The circle passing through the point A intersects the extension of AB at only one point other than A.

True

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False

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Solution

The correct option is A
True

let us assume that the circle intersects AB at two points C and D

Then $∠$ ABC= $180^{\circ}$ and $∠$ ABD should also be $180^{\circ}$ and C and D should lie on a circle which can only be possible if C and D coincide.

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Similar questions

A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is a:

The locus of centers of all circles passing through two given points A and B, is the perpendicular bisector the line segment AB.

Q. A line segment AB intersects a circle at two distinct points C and D as it passes through its centre, as shown in the figure. The line, whose segment is AB, is:

Q. Write 'T' for true and 'F' for false in case of each of the following statements:
(i) Every point has a size.
(ii) A line segment has no length.
(iii) Every ray has a finite length.
(iv) The ray

\vec{A B}

is the same as the ray

\vec{B A}

.
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\bar{A B}

is the same as the line segment

\bar{B A}

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(vi) The line

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is the same as the line

\overset{\leftrightarrow}{B A}

.
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(ix) Two intersecting planes intersect at a point.
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(xii) One and only one line can be drawn to pass through two given points.
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Which of the following statements is false?

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(b) Through two given point, it is possible to draw one and only one straight line.

(d) A line segment can intersect only at one point.

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AB is a line segment in a plane. The circle passing through the point A intersects the extension of AB at only one point other than A.

The correct option is A True let us assume that the circle intersects AB at two points C and D Then ∠ABC=180∘and ∠ABD should also be 180∘ and C and D should lie on a circle which can only be possible if C and D coincide.

The correct option is A
True

let us assume that the circle intersects AB at two points C and D

Then $∠$ ABC= $180^{\circ}$ and $∠$ ABD should also be $180^{\circ}$ and C and D should lie on a circle which can only be possible if C and D coincide.