Question

Please solve 5 a only if you can....​

Answer 1

Answer:  

Exact length: OP = 6*sqrt(2) centimeters

Approximate length: OP = 8.48528 centimeters

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Explanation:

Check out the diagram below. I recreated the diagram in your textbook, but I added on a few other points and segments.

Point E is the midpoint of segment AB. Segment OE is perpendicular to AB.

Point F is the midpoint of CD. Segment OF is perpendicular to CD.

Right triangle AOE forms with OA = 10 as the hypotenuse (radius of the circle) and AE = 8, since E cuts AB in half.

Use the pythagorean theorem to find that...

a^2+b^2 = c^2

(AE)^2 + (OE)^2 = (OA)^2

8^2 + (OE)^2 = 10^2

64 + (OE)^2 = 100

(OE)^2 = 100-64

(OE)^2 = 36

OE = sqrt(36)

OE = 6

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Because chord CD is the same length as chord AB, this means the chords are the same distance from the center point O.

So, OE = OF = 6

Since we have rectangle OEPF, the opposite sides are congruent and we can say OF = EP = 6

Now focus on right triangle OEP. Use the pythagorean theorem again

a^2+b^2 = c^2

(OE)^2 + (EP)^2 = (OP)^2

(6)^2 + (6)^2 = (OP)^2

72 = (OP)^2

(OP)^2 = 72

OP = sqrt(72)

OP = sqrt(36*2)

OP = sqrt(36)*sqrt(2)

OP = 6*sqrt(2)