Question

Determine the value for AB

Answer 1

Answer:  AB = 14

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Explanation:

Use the intersecting chord theorem

AO*OB = DO*OC

2x*10 = (x+3)*8

20x = 8x+24

20x-8x = 24

12x = 24

x = 24/12

x = 2

With that x value in mind, we can find the unknown lengths of each piece of each chord.

• AO = 2x = 2*2 = 4
• DO = x+3 = 2+3 = 5

Then notice how AO*OB = 4*10 = 40 while DO*OC = 5*8 = 40 as well. Both result in the same value (40) which helps verify the correct x value.

To wrap up the problem, we are looking for the length of chord AB, so,

AB = AO+OB = 4+10 = 14

Answer 2

Answer:

x = 2

AB = 14

Step-by-step explanation:

2x(10) = 8(x+3)

20x = 8x + 24

subtract 8x from both sides

12x = 24

x = 2

Check:

4(10) = 8(5)

40 = 40

Correct

2x = 2 x 2 = 4

4 + 10 = 14

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-Chetan K