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3 years ago

What is the length of DE?

Mathematics

1 answer:

miskamm [114]3 years ago

5 0

Answer:

Step-by-step explanation:

If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.

AC *CB = CD CE

4 * (10-4) = CD * 8

4 * 6 = 8 *CD

24 = 8 CD

Divide each side by 8

24/8 = CD

3 = CD

We want the length DE

DE = CD + CE

= 3 + 8

DE = 11

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What is the value of r? Please answer in exact value

sattari [20]

We have three different ways to the solution.

1.
It's a right triangle and isosceles triangle.
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h - the hypotenuse
a - the leg

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2.
Use the Pythagorean theorem:

$r^2=4^2+4^2\\r^2=16+16\\r^2=16\cdot2\\r=\sqrt{16\cdot2}\\r=\sqrt{16}\cdot\sqrt2\\r=4\sqrt2$


3.
Use trigonometric function:

$\sin45^o=\dfrac{4}{r}\\\\\sin45^o=\dfrac{\sqrt2}{2}\to\dfrac{4}{r}=\dfrac{\sqrt2}{2}\ \ \ |cross\ multiply\\\\r\sqrt2=8\ \ \ |\cdot\sqrt2\\\\2r=8\sqrt2\ \ \ |:2\\\\r=4\sqrt2$

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Read 2 more answers

Melanie made a circular necklace. She puts beads evenly spaced around the necklace. If the 4th bead is directly across from the

Tpy6a [65]

Its 12, becuse if its a Circle then you can look at it the same way you look at a clock which has 12 numbers on it and 4 and 11 are directly across each other.

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