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.

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Solution

We know tangents from external point to circle are circle,
So,
$\Rightarrow A Q = Q P (1)$
$Q B = Q P (2)$
From $1$ and $2$
$\Rightarrow A Q = Q B$
Hence, proved.

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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.

We know tangents from external point to circle are circle,So, ⇒AQ=QP(1) QB=QP(2)From 1 and 2⇒AQ=QBHence, proved.

We know tangents from external point to circle are circle,
So,
$\Rightarrow A Q = Q P (1)$
$Q B = Q P (2)$
From $1$ and $2$
$\Rightarrow A Q = Q B$
Hence, proved.