Q. 5. If a chord is drawn through the point ofcontact of the tangent t

1.	Q. 5. If a chord is drawn through the point ofcontact of the tangent to a circle then prove that theangles formed by this chord with the given tangentsare equal to the angles formed in the alternate
Answer» A chord AB of a circle and a line PAQ. Such thatangle BAQ=angle ACB where c is any point in the alternate segment ACB. To Prove:- PAQ is a tangent to the circle. Construction:- Let PAQ is not a tangent then let us draw P' AQ' another tangent at A. Proof: - AS P ’AQ’ is tangent at A and AB is any chord angle BAQ'=angle ACB Butangle BAQ=angle BAQ(given) hence angle BAQ=angle BAQ' Hence AQ' and AQ are the same line i.e. P' AQ' and PAQ are the same line. Hence PAQ is a tangent to the circle at A.

Q. 5. If a chord is drawn through the point ofcontact of the tangent to a circle then prove that theangles formed by this chord with the given tangentsare equal to the angles formed in the alternate

Answer»

A chord AB of a circle and a line PAQ. Such thatangle BAQ=angle ACB where c is any point in the alternate segment ACB.

To Prove:- PAQ is a tangent to the circle.

Construction:- Let PAQ is not a tangent then let us draw P' AQ' another tangent at A.

Proof: - AS P ’AQ’ is tangent at A and AB is any chord

angle BAQ'=angle ACB

Butangle BAQ=angle BAQ(given)

hence angle BAQ=angle BAQ'

Hence AQ' and AQ are the same line i.e. P' AQ' and PAQ are the same line.

Hence PAQ is a tangent to the circle at A.