A chord of the larger among two concentric circles is of length 20 cm and it is tangent to the smaller circle. What is the area (in cm²) of the annular portion between the two circles?

Question

Accepted Answer

Given two concentric circles, the chord of the larger circle is tangent to the smaller circle.

Step 1: Let the radius of the smaller circle be r and the radius of the larger circle be R.

Step 2: The chord of the larger circle is tangent to the smaller circle, so the distance from the center to the chord equals r (radius of smaller circle).

Step 3: The length of the chord is 20 cm.

Step 4: The perpendicular distance from the center to the chord is r, and half the chord length is 10 cm.

Step 5: Using the right triangle formed by the radius R, half chord length, and the perpendicular distance r:

R² = r² + 10²

Step 6: The area of the annular region between the two circles is:

Area = π(R² - r²)

From step 5, R² - r² = 10² = 100

Therefore, area = π × 100 = 100π cm².

Answer

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