Question

please solve fast circles lesson class 10​

Answer 1

$\large\underline{\sf{Solution-}}$

We know that, Length of tangents drawn from external point are equal.

Since, A is external point and AD and AF are tangents from A.

$\rm\implies \:AD = AF - - - (1)$

Also, B is external point and BD and BE are tangents from B.

$\rm\implies \:BD = BE - - - (2)$

Also, C is external point and CE and CF are tangents from C.

$\rm\implies \:CE = CF - - - (3)$

Now, According to statement, It is given that

$\rm \: AB = AC$

can be rewritten as

$\rm \: AD + BD = AF + CF$

can be rewritten as using equation (1), we get

$\rm \: AD + BD = AD + CF$

$\rm \: BD = CF$

Now, using equation (2) and (3), we get

$\rm \: BE = CE$

Hence, Proved

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Additional Information :-

1. Radius and tangent are perpendicular to each other.

2. Tangents are equally inclined to the line joining the center and external point.

3. Perpendicular drawn from centre bisects the chord.

4. Only one tangent can be drawn at a point on a circle.