Mathematics, 13.10.2019 22:30 sherlock19

Ab=diameter of the circle o. oc=radius. arc axb is an arc of the circle with centre c. prove areas of the shaded region are =

Ab=diameter of the circle o. oc=radius. arc axb is an arc of the circle with centre c. prove areas o

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Answer from: xxaurorabluexx

1.
Draw a circle with center C And radius CA, as shown in the attached picture.

Let the lengths of radii AO, OB, OC be R. Triangle ABC is inscribed in the circle with center O and one of its sides is a diameter, this means that the angle ACB is a right angle.
|AO|=|OC|=R, by the Pythagorean theorem |AC|= $\sqrt{2}R$ .

these are all shown in the picture.

2.

Area of triangle ABC is 1/2 * 2R * R= R^2

3.

Let the area between arc BXA and chord AB be Y. (the yellow region).

and let G be the shaded region between arcs AB and AXB.

G=1/2(Area circle with center O)-Y
= $\frac{1}{2} \pi R^{2}-Y$

To find Y:

Notice that the area of the sector ACB is 1/4 of the area of circle with center C, since m(ACB) is 1/4 of 360 degrees.

So Area of sector ACB = $\frac{1}{4} \pi (\sqrt{2} R)^{2}=\frac{1}{4} \pi*2 R^{2} =\frac{1}{2} \pi R^{2}$

Y =area of sector ABC-Area(triangle ABC)= $\frac{1}{2} \pi R^{2}- \frac{1}{2}*2R*R=\frac{1}{2} \pi R^{2}- R^{2}$

4.

Finally,

$G=\frac{1}{2} \pi R^{2}-Y=\frac{1}{2} \pi R^{2}-(\frac{1}{2} \pi R^{2}- R^{2})=R^{2}$

This proves that the 2 shaded regions have equal area.

Ab=diameter of the circle o. oc=radius. arc axb is an arc of the circle with centre c. prove areas o

Ab=diameter of the circle o. oc=radius. arc axb is an arc of the circle with centre c. prove areas o

Answer from: Quest

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

Answer from: Quest

answer: rolling a number cube and flipping a coin.

step-by-step explanation:

Will mark brainliest if you answer a few easy questions! asap! !

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Ab=diameter of the circle o. oc=radius. arc axb is an arc of the circle with centre c. prove areas o...

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