Question

how can i solve this question ?
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Answer 1

Answer:

24

Step-by-step explanation:

We know that AOE equal 18 and EC equal 8. That emans that AEC equal 26.

O is the center of the circle, By definition of the circle, OA, OD,OC and OB are all radii, by definition of a radius and are equal to each other.

Since OA and OC are radii, they form the diameter AEC so they both split the diameter, which is 26 into two equal parts. So OA length is 13, and OC length is 13.

Let's find the length of OE. OC measures 13, EC measures 8 so the the length of OE is 13-8=5.

Remeber that a chord is perpendicular to the radius. So let draw line segment OD. We know have a right triangle OED. We know OD is the radii so the length is 13. OE length is 5 so we can apply Pythagoren Theorem.

${5}^{2} + {x}^{2} = {13}^{2}$

$25 + {x}^{2} = 169$

${x}^{2} = 144$

$x = 12$

So the length of DE is 12. OEB also forms a right triangle since OEB and ODE share two side lengths and a right angle, they are similar triangles so EB length is 12.

So DEB length is 24.