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

Mathematics

1 answer:

BabaBlast [244]3 years ago

3 0

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

You might be interested in

Can someone please help with this math question:)

Bingel [31]

Solution:

The rationalisation factor for $\frac{1}{ a - \sqrt{b} }$ is $a + \sqrt{b}$

So, let us apply it here.

$\frac{1}{5 - \sqrt{2} }$

The rationalising factor for 5 - √2 is 5 + √2.

Therefore, multiplying and dividing by 5 + √2, we have

$= \frac{1}{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } \\ = \frac{5 + \sqrt{2} }{(5 - \sqrt{2})(5 + \sqrt{2} ) } \\ = \frac{5 + \sqrt{2} }{ {(5)}^{2} - ( \sqrt{2})^{2} } \\ = \frac{5 + \sqrt{2} }{25 - 2} \\ = \frac{5 + \sqrt{2} }{23}$