Answer:
see explanation
Step-by-step explanation:
the shaded area is calculated as
outer circle area - inner circle area
since CAB is a tangent to the inner circle at A then OAB = 90° and
Δ OAB is right
using Pythagoras' identity in the right triangle to express R in terms of r and d , then
R² = d² + r²
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A( outer Δ ) = πR² = π(d² + r² ) = πd² + πr²
A ( inner Δ ) = πr²
Then
shaded area = πd² + πr² - πr² = πd²
