Question

Two circle touch each other internally in apoint A.The Radius of the smaller circle with centre M is 5.The dmaller circle passed through the centre N of the larger circle.the tangent to the smaller circle drawn through C intersect the larger circle.in point .Find CD

Answer 1

yadu green circle is bigger and the yellow circle is smaller. the rhythmic is the radius of the big circle which is equal to the green line .
the blue line is the radius of the small circle. the red line is 10. the blue line is 5. the green line is also 10.
you must mention the diagram .
from here you can easily find your answer.
next time attach the figure.

Answer 2

CD = 40√2/3

Step-by-step explanation:

The radius of the smaller circle with centre M is 5

=> AM = MN = MP = 5cm

AN = AM + MN = 10 cm

N is center of Larger circle

=> CN = AN = 10 cm

CM = CN + NM = 10 + 5 = 15 cm

MP = 5 cm

=> CP² = CM² - MP²

=> CP² = 15² - 5²

=> CP² = 200

=> CP = 10√2

ΔCPM ≈ ΔCDA

as ∠C = ∠C ( common)

∠CPM = ∠CDA = 90°     (∠CPM - Tangent    ∠CDA formed by diameter CA)

CP/CD =  CM/CA

=>  10√2 /CD  =  15/20

=> 10√2 /CD  =  3/4

=> CD = 40√2/3

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