Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal. - Noon Academy

Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.

Class 10 | Exercise 18A | ICSE | Maths | Selina | Tangents and Intersecting Chords

Two circles touch each other externally at point P. Q is a point on the common tangent through P. Prove that the tangents QA and QB are equal.

Selina Solutions Concise Class 10 Maths Chapter 18 ex. 18(A) - 3

Solution:

Suppose,

$Q$

be the point from which,

$QA\text{ }and\text{ }QP$

are two tangents with centre

$O$

So,

$QA\text{ }=\text{ }QP\text{ }\ldots ..\left( a \right)$

Similarly, from point

$Q,\text{ }QB\text{ }and\text{ }QP$

are two tangents with centre

$O$

So,

$QB\text{ }=\text{ }QP\text{ }\ldots \ldots \left( b \right)$

From

$\left( a \right)\text{ }and\text{ }\left( b \right),$

we have

$QA\text{ }=\text{ }QB$

So, tangents

$QA\text{ }and\text{ }QB$

are equal.

– Hence Proved

i

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