Define a tangent to a circle.

In geometry, a tangent to a circle is a straight line that only touches or intersects the circle at one point. A tangent is a line that never passes through the centre of the circle. A circle with a point X is depicted in the diagram below. A tangent C has been drawn from X . This is an example of a circle tangent.

Prove that the lengths of tangents drawn from an external point to a circle are equal.

Let A P and A Q are two tangents from an external point A to a circle with centre O . To Prove: A P = A Q The figure from the question can be drawn as follows. Join O P , O Q and O A . We know that, a tangent at any point on a circle is perpendicular to the radius through the point of contact. Here, A P is a tangent and O P is the radius of the circle through P . ∴ O P ⊥ A P Similarly, O Q ⊥ A Q ⇒ ∠ O P A = ∠ O Q A = 90 ° . . . ( i ) In Δ O P A and Δ O Q A , we have O P = O Q [ radii of a same circle ] ∠ O P A = ∠ O Q A = 90 ° [from Eq. (i)] O A = O A [common sides] So, Δ O P A ≅ Δ O Q A [ by R.H.S Congruence rule] ∴ A P = A Q [by CPCT] Hence, proved.

E M B I B E

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Circles>meghalaya board-2019>Q 3

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How many tangents can be drawn from a point outside the circle?

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Important Questions on Circles

HARD

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Circles>meghalaya board-2019>Q 4

In the given figure,

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find $P T$ in $cm$ , if $O P = 41 cm$ and $O T^{'} = 9 cm$ .

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Circles>meghalaya board-2019>Q 5

Define secant of a circle.

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Circles>meghalaya board-2019>Q 6

A tangent to a circle is _____ to the radius through the point of contact.

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Circles>meghalaya board-2020>Q 7

Find the distance between two parallel tangents of a circle of radius

8 cm

.

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Circles>meghalaya board-2020>Q 8

$P Q$ and $P T$ are tangents to a circle with centre $O$ and radius $5 cm$ . If $P Q = 12 cm$ , then prove that the perimeter of the quadrilateral $P Q O T$ is $34 cm$ .