The length of each of two tangents drawn from an external point to a circle is 10 cm. What is the approximate distance from the external point to the center of the circle, if the radius is 6 cm?
Given:
Length of tangent from external point = 10 cm
Radius of the circle = 6 cm
Formula Used:
If tangents are drawn from an external point P to a circle with center O and point of contact T, then:
OP² = OT² + PT²
Solution:
Here,
OT = 6 cm
PT = 10 cm
OP² = 6² + 10²
OP² = 36 + 100
OP² = 136
Taking square root:
OP = √136 ≈ 11.66 ≈ 12 cm
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The length of each of two tangents drawn from an external point to a circle is 10 cm. What is the approximate distance from the external point to the center of the circle, if the radius is 6 cm?
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The distance between the centers of two circles is d. The lengths of their direct and transverse common tangents are L and M, respectively. If L² + M² = 200 and the sum of the squares of their radii is 100, what is the value of d?
