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In the Figure of Question 9; If Ab = Ac Then Prove that Bq = Cq. - 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

In the figure of Question 9; If AB = AC then prove that BQ = CQ.

Solution

Since, from A, AP and AR are the tangents to the circle
Therefore, AP = AR
Similarly, we can prove that

BP = BQ and CR = CQ
Adding,
AP + BP + CQ = AR + BQ + CR
(AP + BP) + CQ = (AR + CR) + BQ
AB + CQ = AC + BQ
But AB = AC
Therefore, CQ = BQ or BQ = CQ

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Solution In the Figure of Question 9; If Ab = Ac Then Prove that Bq = Cq. 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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