Question

in the figure M is the point of contact of two internal touching circles the chord cd of the bigger circle touches the smaller circle at point and line a and b is the common tangent prove a mn bisects 6 angle CMD

Answer 1

Answer:

Attached above hope you satisfied with my answer.

Please mark as brainly.

Answer 2

Explanation:

Let O be the center of the smaller circle.

Let O' be the center of the larger circle.

To prove that MN bisects angles CMD

From the figure, it is obvious that the CD is the chord of the bigger circle.

Also, given that line AMB is a common tangent to both the circles.

The line from the center of the circle to the tangent makes an angle 90°

Thus, we have,

O'N ⊥ CD, ON⊥CD, OM⊥AB

Hence, we have,

CN = ND

Since, the line from the center of the circle to the tangent makes an angle 90°

Thus, we have,

∠CNM=∠DNM= 90°

Also, the line NM = MN is common side.

Therefore, by SAS property,

$\triangle \mathrm{CNM} \cong \triangle \mathrm{DNM}$

Thus,  ∠CMN=∠DMN

Therefore, MN bisects angles CMD

Hence proved

Learn more:

(1) In the figure, M is the point of contact of two internally touching circles. The chord CD of the bigger circle touches the smaller circles at point N. Line AMB is their common tangent. Prove MN bisect angle CMD​

brainly.in/question/8280759

(2) Two circles touch each other externally at P. AB is a common tangent to the circle touching them at A and Ben. find angle APR.

brainly.in/question/2021764