CK12 - Geometry

Theremustbe anotherpoint on the tangentline suchthat is perpendicularto the tangentline.

Therefore,in the right triangle , is the hypotenuseand is a leg of the triangle.However,

this is not possiblebecause. (Notethat lengthof the radius ).

Sinceour assumptionled us to a contradiction,this meansthat our assumptionwas incorrect.Therefore,

the tangentline mustbe perpendicularto the radiusof the circle.

Sincethe tangentto a circleand the radiusof the circlemakea right anglewith eachother, we can often
use the PythagoreanTheoremin orderto find the lengthof missingline segments.

Example 1

In the figure,

is tangentto the circle.Find

.

Since is tangentto the circle,then.

This meansthat is a right triangleand we can applythe PythagoreanTheoremto find the length

of.

Example 2

Markis standingat the top of Mt. Whitney, whichis

feet tall. The radiusof the Earthis approximately

miles.(Thereare