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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

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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#### Video TutorialsVIEW ALL [1]

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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