Three key properties of tangent lines to circles

Finding angle DCE using isosceles triangle properties

Finding angle CBD using tangent perpendicularity and inscribed angle theorem

Finding angle BAD using tangent and isosceles triangle properties

Finding the diameter using the radius and tangent line

Proving triangle CBD is a right triangle using inscribed angle theorem

Using the Pythagorean theorem to find chord length CD

Finding angle ABC using the tangent-radius perpendicularity property

Finding segment AC using the Pythagorean theorem

Identifying triangle BOD as equilateral using radii

Hammer throw problem using tangent line and Pythagorean theorem