تحميل صور
in the figure above O is the center of the circle
The segment PA is tangent to the circle
also:
AG parallel to HF
the angle FOH=140 degree
the angle AOH=30 degree
DOG=DOF
what is the measure of angle P?
تحميل صور
in the figure above O is the center of the circle
The segment PA is tangent to the circle
also:
AG parallel to HF
the angle FOH=140 degree
the angle AOH=30 degree
DOG=DOF
what is the measure of angle P?
1. Since $\displaystyle \overline{GA} \parallel \overline{FH}$ and these line segments are chords of the same circle there exists a common axis of symmetry passing through O.
2. Therefore $\displaystyle \angle(FOG) = \angle(AOH)$ and consequently the angle
$\displaystyle \angle(GOA) = 360^\circ - 140^\circ - 2 \cdot 30^\circ = 160^\circ$
3. The sum of the interior angles in a quadrilateral is 360°. Therefore
$\displaystyle \angle(APE) = 360^\circ - 160^\circ - 2 \cdot 90^\circ = 20^\circ$
The perpendicular bisector of one chord is the perpendicular bisector of the other chord too. This bisector is a symmetry-axis of both chords, of the circle and consequently of the two angles of 30° which are left unmarked.
The symmetry-axis is drawn in red in the attached diagram.