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Two Circle 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. - ICSE Class 10 - Mathematics

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ConceptTangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments

Question

Two circle 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.

Solution

From Q, QA and QP are two tangents to the circle with centre O
Therefore, QA = QP.....(i)
Similarly, from Q, QB and QP are two tangents to the circle with centre O'
Therefore, QB = QP ......(ii)
From (i) and (ii)
QA = QB
Therefore, tangents QA and QB are equal.

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Solution Two Circle 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. Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.
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