1) 2 circles touch internally at point P From a point T on the common tangent at P, tangent - Maths - Circles

Question

1) 2 circles touch internally at point P From a point T on the
common tangent at P, tangent segments TQ and TR are drawn to the
circles Prove that TQ =TR

Sunanta Meitei · Accepted Answer

Hi!
Here is the answer to your question
Given: Circles with centers C1 and
C2 touch each other internally at P TP is the common
tangent to the circles TQ and TR is a tangent to circle with
centres C1 and C2, respectively
To prove: TQ = TR
<img src=
"https://s3mn%20mnimgs%20com/img/shared/userimages/mn_images/image/Ce%20png"
alt="">
Proof:
TP and TQ are tangents drawn from an external point T to the
circle with centre C1
So, TQ = TP … (1) (length of
tangents drawn from external point to circle are
equal)
Similarly, considering the smaller circle,
TR = TP … (2)
From (1) and (2), we get
TQ = TR
Cheers!

1) 2 circles touch internally at point P. From a point T on the common tangent at P, tangent segments TQ and TR are drawn to the circles. Prove that TQ =TR.