Answer:
Step-by-step explanation:
a) A diameter is a straight line that bisects a circle through its center. Line AD serves as a diameter.
The radius is half that of the diameter, which means AD/2 = AO or OD
A chord connects two points on the circumference of a circle but does not come through the center; it traverses segments of the circle instead. For instance, line FH is a chord
A tangent touches the circumference of the circle at one specific point and can contact any point along the circle's edge. Examples of tangent lines include AB and DE.
b) It's essential to know that the angles around a point or within a circle total 360°.
<EOH + <ECH = 360°
If <EOH = 131°
then <ECH = 360° - 131°
which results in <ECH = 229°
- <EFH is situated within the circle's circumference. Additionally, the angle at a circle's center is double that of the angle at the circumference. Therefore, since <EOH is at the circle’s center, <EFH = <EOH/2
Thus, <EFH = 131/2
so <EFH = 65.5°
c) Since AB = DE, it follows that <AB = <DE (equal and opposite angles). Given <AOB = 20°, then <DE = 20°
d) According to the illustration, <GFD = <GLD
If <GFD = 126°, then <GLD will likewise be 126°
e) Let HK = x+4, FK = x+14, GK = x, and CK = x+32
From the figure, we have CG = CK + KG
This means CG = x+32+x
leading to CG = 2x+32
Also, FH = FK + HK
So, FH = x+14+x+4
thus FH = 2x+18
