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In the figure, CD is a tangent, AB is 7cm, CD is 12 cm, find the value of BC.

In the figure, CD is a tangent, AB is 7cm, CD is 12 cm, find the value of BC.-example-1
User Greg Ross
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1 Answer

5 votes

Answer:

BC = 9 cm

Explanation:

given a tangent and a secant drawn from an external point to the circle then the square of the measure of the tangent is equal to the product of the secants external part and the entire secant.

let BC = x , then

x(x + 7) = 12²

x² + 7x = 144 ( subtract 144 from both sides )

x² + 7x - 144 = 0 ← in standard form

(x - 9)(x + 16) = 0 ← in factored form

equate each factor to zero and solve for x

x - 9 = 0 ⇒ x = 9

x + 16 = 0 ⇒ x = - 16

however , x must be greater than zero, then x = 9

that is BC = 9 cm

User Alok Patel
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