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THEOREM -14 CONVERSE OF Alternate segment Theorem Statement:- “If a line is drawn through an end point of a chord of a circle so that the angle formed.

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Presentation on theme: "THEOREM -14 CONVERSE OF Alternate segment Theorem Statement:- “If a line is drawn through an end point of a chord of a circle so that the angle formed."— Presentation transcript:

1 THEOREM -14 CONVERSE OF Alternate segment Theorem Statement:- “If a line is drawn through an end point of a chord of a circle so that the angle formed with the chord is equal to the angle substended by the chord in the alternate segment, then the line is a tangent to the circle”. C B A x1 XY y1 o

2 Given:- circle with centre “O” XAY is a line meeting chord AB at A. and C is the point in the other segment such that BAY = ACB. C B A x1 XY y1 o

3 R.T.P:- XAY is tangent to the circle Construction:- NIL C B A x1 XY y1 o

4 Proof:- suppose XAY is not tangent to the circle. Let X‘AY’ is tangent to the circle Let X‘AY’ is tangent to the circle ACB = BAY (1) C B A x1 XY y1 o

5 But ACB = BAY (given) (2) From (1) & (2) BAY = BAY which is possible iff XAY coincides with XAY XAY is tangent to the circle at A. C B A x1 XY y1 o

6 Conclusion:- “If a line is drawn through and end point of a chord of a circle so that the angle formed with the chord is equal to the angle substended by the chord in the alternate segment, then the line is a tangent to the circle”. C B A x1 XY y1 o


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