If two chords AB, CD intersect each other at O and AO = 9 cm, BO = 4 cm, CO = $10 + x$ cm, DO = $10 - x$ cm. Fine the value of $x$ .

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Solution

The correct option is C
8

We know that

$A O \times B O = C O \times D O$

$9 \times 4 = (10 + x) \times (10 - x)$

$36 = 10^{2} - x^{2}$ ______ using formula ( $a + b) (a - b) = a^{2} - b^{2}$

$x^{2} = 100 - 36$

$x^{2} = 64$

$x = 8, - 8$

Taking only positive value for length, we get x = 8 cm

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If two chords AB, CD intersect each other at O and AO = 9 cm, BO = 4 cm, CO = 10+x cm, DO = 10−x cm. Fine the value of x.

The correct option is C 8 We know that AO×BO=CO×DO 9×4=(10+x)×(10−x) 36=102−x2 ______ using formula (a+b)(a−b)=a2−b2 x2=100−36 x2=64 x=8, −8 Taking only positive value for length, we get x = 8 cm

If two chords AB, CD intersect each other at O and AO = 9 cm, BO = 4 cm, CO = $10 + x$ cm, DO = $10 - x$ cm. Fine the value of $x$ .

The correct option is C
8

We know that

$A O \times B O = C O \times D O$

$9 \times 4 = (10 + x) \times (10 - x)$

$36 = 10^{2} - x^{2}$ ______ using formula ( $a + b) (a - b) = a^{2} - b^{2}$

$x^{2} = 100 - 36$

$x^{2} = 64$

$x = 8, - 8$

Taking only positive value for length, we get x = 8 cm