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katovenus [111]
3 years ago
13

Find the value of x - this is circle segments.

Mathematics
1 answer:
Ne4ueva [31]3 years ago
6 0

Given:

Diagram of a circle and its two secant from an exterior point.

To find:

The value of x.

Solution:

We know that, If two secant are on a circle from an exterior point, then the products of measure of secants and measure of external segments of secants are equal.

Using the above property, we get

(x+7)x=(2+2)2

x^2+7x=(4)2

x^2+7x=8

x^2+7x-8=0

Splitting the middle term, we get

x^2+8x-x-8=0

x(x+8)-1(x+8)=0

(x+8)(x-1)=0

Using zero product property, we get

(x+8)=0 and (x-1)=0

x=-8 and x=1

Side cannot be negative.

Therefore, the only possible value of x is 1.

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