If from any point on the common chord of two intersecting circles, tangents are drawn to circle. Prove that they are equal.
Answers
Answered by
3
Consider the two circles intersect at points X and Y. XY is the common chord.
Suppose A is a point on the common chord and AM and AN be the tangents drawn from A to the circle.
AM is the tangent and AXY is a secant.
∴ AM2 = AX × AY .......................(1) [ From the theorem]
AN is the tangent and AXY is a secant.
∴ AN2 = AX × AY ..................(2) [ From the theorem]
From (1) and (2), we get
AM2 = AN2
∴ AM = AN
Suppose A is a point on the common chord and AM and AN be the tangents drawn from A to the circle.
AM is the tangent and AXY is a secant.
∴ AM2 = AX × AY .......................(1) [ From the theorem]
AN is the tangent and AXY is a secant.
∴ AN2 = AX × AY ..................(2) [ From the theorem]
From (1) and (2), we get
AM2 = AN2
∴ AM = AN
ManushkasinghM:
Can you please tell the theorem used?
if a two tangents are drawn from an same point then they r always equal
Well, thanks!
no need
Similar questions