in the following figure , two circles touch each other internally in a point A . The radius of the smaller circle with centre M is 5. The smaller circle passed through the centre N of the larger circle . The tangent in the smaler circle drawn through c intersects the larger circle in point d find cd
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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°
CP/CD = CM/CA
=> 10√2 /CD = 15/20
=> 10√2 /CD = 3/4
=> CD = 40√2/3
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