Chapter 10.6, Problem 25PSC

To determine

Give the explanation for the given proof.

Answer to Problem 25PSC

The value of $mArc\left(HM\right)={120}^{°}$ .

Explanation of Solution

Given:

The given data is the $\Delta ABC$ is a inscribed in $\odot P$ .

  $AE\perp BC$

  $\overline{CD}\perp \overline{AB}$

The given proof is $Arc\left(BD\right)\cong Arc\left(BE\right)$ .

Calculation:

Draw a diagram using given data.

  

The vertically opposite angle are equal in measurement.

  $m\angle AOF=m\angle GOC=x$ (let)

  $m\angle AFO=m\angle CGO={90}^{°}$ (given)

In triangle $\Delta AFO$

  $m\angle OAF={90}^{°}-x$

In triangle $\Delta CGO$

  $m\angle GCO={90}^{°}-x$

Now,

  $m\angle OAF=m\angle GCO$

In a circle, the arcs inscribed a same angle are congruent.

Hence $Arc\left(BD\right)\cong Arc\left(BE\right)$ .