Question

Find the value of x. A: 15 B: 12 C: 10 D: 8

Answer 1

Answer:

$\boxed{\sf C. \ 10}$

Step-by-step explanation:

$\sf The \ intersecting \ chord \ theorem \ states \ that \ the \ products$

$\sf of \ the \ lengths \ of \ the \ line \ segments \ on \ each \ chord \ are \ equal.$

$NH \times HT = MH \times HY$

$(x+20) \times 8=12 \times 20$

$\sf Expand \ brackets \ and \ multiply.$

$8x+160=240$

$\sf Subtract \ 160 \ from \ both \ sides.$

$8x+160-160=240-160$

$8x=80$

$\sf Divide \ both \ sides \ by \ 8.$

$\displaystyle \frac{8x}{8} =\frac{80}{8}$

$x=10$

Answer 2

The value of x is 10.

We have a circle and inside it two chords MY and NT intersect at point H.

We have to find the value of x in the figure.

What is intersecting chord theorem?

According to the intersecting chord theorem, when two chords say AB and CD intersect at point O, then

AO x OB = CO x OD

Applying the chord intersecting theorem to the figure in the question, we get -

MH x HY = NH x HT

12 x 20 = (x+20) x 8

240 = 8x + 160

8x = 80

x = 10

Hence the value of x is 10.

To solve more questions on Circles and chords, visit the link below -

https://brainly.com/question/15568573

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