Find the value of x - Secant and Tangent Angles in Circles

Mathematics

1 answer:

VladimirAG [237]3 years ago

6 0

Answer:

C. 70°

Step-by-step explanation:

The inscribed angle marked 15° intercepts an arc that is double that measure, so the intercepted arc on the right is 2×15° = 30°.

The external angle marked 20° is half the difference of the intercepted arcs, so is ...

20° = (1/2)(x - 30°)

40° = x - 30° . . . . . . multiply by 2

70° = x . . . . . . . . . . . add 30°

The value of x is 70°.

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In circle o,find the value of x, rounded to the nearest tenth.

Gemiola [76]

Answer:

$\huge\boxed{x \approx 5.4}$

Step-by-step explanation:

We can break down this problem by first realizing different parts of the circle.

The line which is 8 units long is a chord of the circle.
The line that is 3.6 is almost the radius of the circle
The line that x sits on is the radius.

With this, we can find out if we find the radius of the circle, we have our answer.

We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.

What we need is a way to find the radius of the circle. This will get us x. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.

If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).

We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:

$\displaystyle a^2 + b^2 = c^2$

Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!

$3.6^2 + 4^2 = c^2$
$12.96+16=c^2$
$28.96=c^2$
$\sqrt{28.96} = c$
$5.4 \approx c$

Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.

The line X does just that. Therefore, the value of x is also 5.4.

Hope this helped!