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P is the Mid – Point of an Arc Apb of a Circle. Prove that the Tangent Drawn at P Will Be Parallel to the Chord Ab. - ICSE Class 10 - Mathematics

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ConceptTangent Properties - If a Chord and a Tangent Intersect Externally, Then the Product of the Lengths of Segments of the Chord is Equal to the Square of the Length of the Tangent from the Point of Contact to the Point of Intersection

Question

P is the mid – point of an arc APB of a circle. Prove that the tangent drawn at P will be parallel  to the chord AB.

Solution

Join AP and BP.
Since TPS is a tangent and PA is the chord of the circle.
`∠`BPT =  `∠`PAB (angles in alternate segments)
But

`∠`PBA = `∠`PAB (∵ PA = PB ) 

∴ `∠` BPT =`∠`PBA

  But these are alternate angles

∴ TPS ll AB 

  Is there an error in this question or solution?

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Solution P is the Mid – Point of an Arc Apb of a Circle. Prove that the Tangent Drawn at P Will Be Parallel to the Chord Ab. Concept: Tangent Properties - If a Chord and a Tangent Intersect Externally, Then the Product of the Lengths of Segments of the Chord is Equal to the Square of the Length of the Tangent from the Point of Contact to the Point of Intersection.
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