Given that OT =5, XT=12, and OX= 13 is XY tangent to circle O at T? Explain.

Mathematics

1 answer:

strojnjashka [21]2 years ago

5 0

As, 5, 12 and 13 form a pythagorean triplet.
Which means OTX is a right angles trangle right angles at T.

Which means angle OTX = 90° .

Which means

Yes XY is a tangent.

Because A tangent makes 90° angle with the radius at that point of contact.

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In the figure, angle ZYX is measured in degrees. The area of the shaded sector can be determined using the formula StartFraction

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The given options are:

(A)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

(B)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the circumference of the circle will yield the area of the sector.

(C)the central angle measure of the sector multiplied by the area of the circle will yield the area of the sector.

(D)the central angle measure of the sector multiplied by the circumference of the circle will yield the area of the sector.

Answer:

(A)the central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

Step-by-step explanation:

The area of the shaded sector can be determined using the formula:

$\frac{m\angle ZYX}{360^\circ} \cdot \pi r^2$