How to find common tangent of two circles?
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Step 1: Find the coordinates of centres C1, C2 and radii r1, r2 of the two given circles.
Step 2: Find the coordinates of the point, say P dividing C1C2 externally in the ratio r1 : r2 Let P ≡ (h, k).
Step 3: Write the equation of any line through P (h , k) i.e. y − k = m(x − h) ….(1)
Step 4: Find the two values of m, using the fact that the length of the perpendicular on (1) from the centre C1 of one circle is equal to its radius r1
Step 5: Substituting these values of ‘ m ‘ in (1), the equation of the two direct common tangents can be obtained.
(b) The transverse common tangents also meet on the line of centres and divide it internally in the ratio of the radii.
Step 2: Find the coordinates of the point, say P dividing C1C2 externally in the ratio r1 : r2 Let P ≡ (h, k).
Step 3: Write the equation of any line through P (h , k) i.e. y − k = m(x − h) ….(1)
Step 4: Find the two values of m, using the fact that the length of the perpendicular on (1) from the centre C1 of one circle is equal to its radius r1
Step 5: Substituting these values of ‘ m ‘ in (1), the equation of the two direct common tangents can be obtained.
(b) The transverse common tangents also meet on the line of centres and divide it internally in the ratio of the radii.
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