Question

A circus ring is the arena where much of the action takes place at a circus. The figure below shows a circus ring with the center O. Arc AB and Arc DE are openings into the circle to enter and exit the ring.

Answer 1

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