If from any point on the …
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Sia ? 6 years, 1 month ago
Let the two circles intersect at points M and N. MN is the chord.
Suppose O is a point on the common chord and OP and OQ be the tangents drawn from A to circle.
OP is the tangent and OMN is a secant.
According to the theorem which says that if PT is a tangent
to the circle from an external point P and a secant to the circle
through P intersects the circle at points A and B, then
PT2=PA×PB
Therefore, OP2=OM×ON ...... (1)
Similarly, OQ is the tangent and OMN is a secant for that also.
Therefore, OQ2=OM×ON ...... (2)
Comparing (1) and (2)
OP2 = OQ2 ⇒OP = OQ
Hence, the length of the 2 tangents is equal.
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