Circle - Tangent for class 10th students and grade x maths and mathematics students

Circles

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Index Introduction to Circles Tangent to a Circle

* Theorem1: The tangent at any point of a circle is perpendicular to the radius through the point of contact.

* Theorem2: A line drawn through the end of a radius and perpendicular to it is a tangent to the circle.

Number of Tangents from a point on a circle * Theorem2: The lengths of the tangent drawn from an external point to a

circle are equal.* Theorem3: If two tangents are drawn to a circle from an external point then,

(i) they subtend equal angles at the centre(ii) they are equally inclined to the line segment joining the center to

that point

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Tangent to Circle

Chapter : Introduction to Trigonometry Website: www.letstute.com

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We already know…

Definition of Circle Circle basics (chord, segment, sector,

arc, secant, etc) Intersecting line, non-intersecting line

and tangent.


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We will learn ….

Tangent to a circle is a line that intersects the circle at only one point

Danish mathematician Thomas Fineke There is only one tangent at a point of the circle The tangent to a circle is a special case of the

secant, when the two end points of its corresponding chord coincide.


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Tangent to a Circle

Tangent: Tangent to a circle is a line that intersects the circle at only one point

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A

C

B

D

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Tangent to a Circle

Activity 1:

.P

. . C

D

The tangent to the circle is a special case of the secant, when the two end points of its corresponding chords coincide.

A

Bll

R3

B .

Bl

. R2

R1

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Q1

. . Q2 . . Q3

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Tangent to a Circle

The word “TANGENT” comes from the Latin word ‘tangere’, which means to touch and was introduced by the Danish mathematician Thomas Fineke in 1583.

Thomas Fincke (6 January 1561 – 24 April 1656)

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Tangent to a Circle

Activity2: P

Q.

. P ll P l .

. .

.

. .

Tangent is the secant when both of the end points of the corresponding chord coincide.

Q l Q ll

The common point of the tangent and the circle is called point of contact.

Point of contact

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Tangent to a Circle

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Now we know…


Tangent to a circle is a line that intersects the circle at one and only one point

Only one tangent can be drawn at a point of the circle

The tangent to a circle is a special case of the secant, when the two end points of its corresponding chord coincide.

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Next video….

Theorem1: The tangent at any point of a circle is perpendicular to the

radius through the point of contact.

Please visit www.letstute.com to view the next video Chapter : Introduction to Trigonometry Website: www.letstute.com

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Education

Circle - Tangent for class 10th students and grade x maths and mathematics students