Tangent chord angle help

[AAlonso]

i havent done math like this in a while and i need a refresher on how this is sloved help

 

[Mrspi]

i havent done math like this in a while and i need a refresher on how this is sloved help

If an angle is formed by two chords that intersect ON the circle (an inscribed angle, vertex ON the circle) or by a tangent and a chord (vertex of the angle is also ON the circle), the measure of the angle is (1/2)*(intercepted arc).

 

[soroban]

Hello, AAlonso!

If you forget that formula, you can still work it out.

The measure of arc \(\displaystyle XY\) is \(\displaystyle 124^o.\)
What is the measure of the tangent-chord angle \(\displaystyle \angle XYZ\) ?

              * * *
          *           *
        *               * X
       *                 o
                      * *
      *        O   * 28*  *
      *         o     *   *
      *         *124 *    *
                *   *       124
       *        *28*     *
        *       * *     *
          *      *    *
      - - - - * o * - - - o Z
                Y

Let \(\displaystyle O\) be the center of the circle.

\(\displaystyle \text{Arc }XY \:=\: 124^o\)
Hence, central angle \(\displaystyle \angle XOY = 124^o\)

Since \(\displaystyle \Delta XOY\) is isosceles:
. . \(\displaystyle \angle OXY \,=\,\angle OYX \,=\,28^o\)

Since \(\displaystyle \angle OYZ = 90^o,\;\angle XYZ = 62^o\)

 

[AAlonso]

Yes i understand how to do this now thank you for the help its been a while since ive done this and it slipped my mind