Two circles touch each other internally Show that the tangents drawn to the 2 circles from any point on - Maths -

Question

Two circles touch each other internally Show that the tangents
drawn to the 2 circles from any point on the common tangent are
equal in length

Chetna Khanna · Accepted Answer

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/discuss_editlive/2316145/2012_01_02_14_32_16/1621098%20png">
Given : AO is a tangent to the circles which
intersect each other internally
Consider the point A,
We construct two tangents AB and AC from point A to the two
circles
Now, AO = AC [Tangents drawn from an external point to the
circle are equal in length]
Also, AB = AO [Tangents drawn from an external point to the
circle are equal in length]
Thus, AB = AC
Hence, tangents drawn to the two circles (touching each other
internally) from any point on the common tangent are equal in
length

Two circles touch each other internally. Show that the tangents drawn to the 2 circles from any point on the common tangent are equal in length.