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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

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?

#### APPEARS IN

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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