Question

(4x-10) Use the diagram above to determine the mCE The mCE-

Answer 1

Answer: Arc CE measures 62 units

Step-by-step explanation: What we have in the question is a circle with two secants ABC and ADE. The two secants have been extended such that two arcs have been formed which are, major arc CE (that is, 4x - 10) and minor arc BD (that is 26).

When you have a circle with two intersecting secants, the angle x (that is angle CAE) is derived as half of the difference of the two intercepted arcs. That is;

Angle x = 1/2 [CE - BD)

Angle x = 1/2 [ (4x - 10) - 26]

Angle x = 1/2(4x - 36)

Cross multiply and we now have

2x = 4x - 36

Collect like terms and we now have

36 = 4x - 2x

36 = 2x

Divide both sides by 2

18 = x

Having calculated x as 18, where arc CE equals 4x - 10, then substitute for the value of x.

CE = 4(18) - 10

CE = 72 - 10

CE = 62