Answer:
Step-by-step explanation:
a) A diameter is a line that cuts a circle through at the centre. Line AD is a diameter.
Radius is half of a diameter i.e AD/2 = AO or OD
Chord is a straight line that touches the circumference of a circle. It doesn't pass through the centre like the diameter but cuts through the segments of a circle. Example of a chord is line FH
A tangent is a line that touches the circumference of a circle at just a point. It can touch any point on the circle. Example of a tangent line are AB and DE.
b) We must know that angle at a point or in a circle is 360°.
<EOH + <ECH = 360°
If <EOH = 131°
<ECH = 360° - 131°
<ECH = 229°
- <EFH falls in the circumference of the circle. Also know that, angle at the centre of a circle is twice angle at the circumference. Since <EOH is at the centre of the circle. <EFH = <EOH/2
<EFH = 131/2
<EFH = 65.5°
c) Given AB = DE, then <AB = <DE (oppositely directed angle).
Given <AOB = 20° then <DE = 20°
d) According to the diagram, <GFD = <GLD
If <GFD = 126°, then <GLD = 126°
e) Given HK = x+4, FK = x+14, GK = x, CK = x+32
From the diagram, CG = CK + KG
CG = x+32+x
CG = 2x+32
Also, FH = FK+HK
FH = x+14+x+4
FH = 2x+18
