Question

cm
In the given figure T is the point of contact of two
circles with centres A and B respectively.
If LAPT = 50°. find the measures of LATP and
ZBQT
A
T т
A​

Answer 1

Let O be the center of smaller circle and O' be center of larger circle.

CD is chord of bigger circle which touches the smaller circle at point N.

Line AMB is common tangent to both the circles.

Postulates to Remember:

1. Perpendicular from center to chord bisects the chord.

2. Line from center of circle to point of contact of tangent makes an angle of 90 degree with the tangent at that point.

O'N ⊥ CD, ON⊥CD, OM⊥AB.

CN=ND

∠CNM=∠DNM=Each being 90°

Line segment NM is common.

ΔCNM ≅ ΔDNM→→[SAS]

So, ∠CMN=∠DMN→→CPCT

Hence , MN bisect angle CMD​.