Determine whether a tangent line to circle O is shown in the

Determine whether a tangent line to circle O is shown in the diagram, for AB = 7.75. OB = 4, and AO = 8.75. Explain your reasoning. (The figure is not drawn to scale.)

Solution

Please note that center is O, given the nomenclature that it\' Circle O.

If a tangent line is shown then the angle between the AB and BO ( which should be the radius) then should be 90

So, 7.75^2 +4^2 = 76.0625

This is equal to AO^2 = 8.75^2 = 76.0625

Hence, AB is a tangent