Circles Geometry: Distance for Three Common Tangents
To determine the minimum distance between the centers of two circles that have exactly three common tangents, we need to understand the relationship between the distance ($d$) between their centers and their radii ($r_1$ and $r_2$).
Condition for Three Common Tangents
Exactly three common tangents exist between two circles when they touch each other externally.
- When circles touch externally, the distance ($d$) between their centers is equal to the sum of their radii ($r_1 + r_2$).
Calculating Minimum Distance
Given:
- Radius of the first circle, $r_1 = 5$ cm
- Radius of the second circle, $r_2 = 3$ cm
For the circles to touch externally, the distance ($d$) between their centers must be:
$d = r_1 + r_2$
Substituting the given radii:
$d = 5 \text{ cm} + 3 \text{ cm}$
$d = 8 \text{ cm}$
Therefore, the minimum distance between the centers of the two circles is 8 cm.
Similar Questions
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Important Questions from Geometry
ABCDEF is a regular hexagon. Side of the hexagon is 36 cm. What is the area of the triangle AOB ?
If ∆ABC ~ ∆DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm 2, then the area of the triangle DEF is:
If Δ ABC is right angled at B, AB = 12 cm and ∠CAB = 60°, determine the length of BC.
If ΔABC and ΔDEF are congruent triangles, then which of the following is FALSE?
D and E are points on the sides AB and AC, respectively, of ΔABC such that DE is parallel to BC and AD ∶ DB = 7 ∶ 9. If CD and BE intersect each other at F. then find the ratio of areas of ΔDEF and ΔCBF.
