The distance between the centres of two circles of radii 22 cm and 10 cm is 37…
2024
The distance between the centres of two circles of radii 22 cm and 10 cm is 37 cm. If the points of contact of a direct common tangent to these circles are M and Q, then find the length of the line segment MQ.
- A.
35 cm
- B.
39 cm
- C.
29 cm
- D.
25 cm
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Correct answer: A
Identify Given Values:
Distance between centers (d) = 37 cm.
Radius of the first circle (r1) = 22 cm.
Radius of the second circle (r2) = 10 cm.
Apply the Formula:
The formula for the length of a direct common tangent is: length = sqrt(d^2 - (r1 - r2)^2).
Calculate the difference between the radii: r1 - r2 = 22 - 10 = 12 cm.
Substitute the values into the formula: length = sqrt(37^2 - 12^2).
Calculate the squares: 37^2 = 1369 and 12^2 = 144.
Calculate the difference: 1369 - 144 = 1225.
Find the square root: sqrt(1225) = 35 cm.