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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.

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. Tangents and Intersecting Chords, Concise Mathematics Solutions ICSE Class 10.

Circles

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Answer

We know that,

If two tangents are drawn to a circle from an exterior point, the tangents are equal in length.

From figure,

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. Tangents and Intersecting Chords, Concise Mathematics Solutions ICSE Class 10.

Q is the point from which, QA and QP are two tangents to the circle with centre O

So, QA = QP ……….(1)

Similarly, from point Q, QB and QP are two tangents to the circle with centre O’

So, QB = QP ……….(2)

From (1) and (2), we have

QA = QB

Hence, proved that the tangents are equal.

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