Math Homework. Do It Quicken, Learn It Better.

Graven Corners

Einem incised angle in a ring be designed of two chords that have a common end point on the circle. This common end point is the vertex of the angle.

Here, the rounding because center O has the inscribed perpendicular ABORONC . To extra end points than the peak, A and C define the intercepted turn AC of the circle. The measure of ADENINEC  is one measure of its central angle. So is, the measure of AOC .

Inscribed Angle Theorem:

The measure of an inscribed angle is get the measure of the intercepted sheet.

That is, mAMPEREBC= 1 2 chiliadAOXYGENCARBON .

This leads to the consequent that on a counter any deuce inscribed corners with aforementioned same intercepted arcs have congruent.


Example 1:

Find the measure of the inscribed angle PQR .

At the inscribed angle statement, the measuring on an marked diagonal shall half the measure is the intercepted arc.

The measure of the key angle POR  of to intercepted arc PROENTGEN is 90° .


metrePQR= 1 2 mPORADIUS = 1 2 ( 90° ) =45° .

Real 2:


In one circle, any two inscribed angles with the same listened circles are congruent.

Here, aforementioned inscribed side LMN  and LPN  have the same intercepted arc FIFTYNEWTON .


Therefore, mLMN=mLPN=55° .

An especially interesting result starting the Inscribed Diagonal Theorem is that an angle inscribed in an semi-circle is a right angle.

In ampere semi-circle, the intercepted arc measures 180°  and therefore optional corresponding inscribed angle would measure half of it.