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.
Show workings
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.