In a circle center O, CBD is a tangent to the circle and BC is 6cm, OC is 10cm. Determine the length of the diameter of the circle.

Question

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Answer 1

First, we can use the fact that CBD is tangent to the circle to determine that angle OBC is a right angle (since the radius of the circle is perpendicular to a tangent line at the point of contact).

Using the Pythagorean theorem in triangle OBC, we have:

OC^2 = OB^2 + BC^2

Substituting OB with its value 2r (where r is the radius of the circle), we have:

10^2 = (2r)^2 + 6^2

Simplifying this equation, we get:

100 = 4r^2 + 36

64 = 4r^2

r^2 = 16

r = 4

Therefore, the diameter of the circle is twice the radius, which is:

2r = 2(4) = 8 cm

Hence, the length of the diameter of the circle is 8 cm.