Result 6 on circles and tangents — lesson. Mathematics State Board, Class 10.

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எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்

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Result $6$ :

The two direct common tangents drawn to the circles are equal in length.

Explanation:

The two direct common tangents

$AC$ and

$BD$ from

$P$ drawn to the circles are equal in length.

$\Rightarrow$

$AC$

$=$

$BD$

Proof of the result:

By the result

$3$ , we have:

The lengths of the two tangents drawn from an exterior point to a circle are equal.

$PA$

$=$

$PB$ and

$PC$

$=$

$PD$ .

Subtract the above two equations.

$PA$

$-$

$PC$

$=$

$PB$

$-$

$PD$

$AC$

$=$

$BD$

Example:

In the above given figure if

$PB$

$=$

$9$

$cm$ and

$AC$

$=$

$6$

$cm$ , find the length of the tangent

$PD$ .

Solution:

By the result, we know that

$AC$

$=$

$BD$ .

So,

$BD$

$=$

$6$

$cm$ .

From the figure it is observed that,

$PD$

$=$

$PB$

$-$

$BD$ .

$PD$

$=$

$9$

$cm$

$-$

$6$

$cm$

$PD$

$=$

$3$

$cm$

Therefore, the length of the tangent

$PD$

$=$

$3$

$cm$ .

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7. Result 6 on circles and tangents

Theory: