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In the given circle, chord \(\overline {AB}\) is extended to meet the tangent \(\overline {DE}\) at D. If  \(\overline {AB}\) = 10 cm and \(\overline {DE}\) 12 cm, what is the length of  B̅D̅?

In the given circle, chord \(\overline {AB}\) is extended to meet the tangent \(\overline {DE}\) at D. If  \(\overline {AB}\) = 10 cm and \(\overline {DE}\) 12 cm, what is the length of  B̅D̅? Correct Answer 8 cm

⇒ Let BD = x

⇒ Formula, DE2 = DB × DA

122 = x(x + 10)

⇒ 144 = x2 + 10x

⇒ 0 = x2 + 10x - 144

⇒ 0 = x2 + 18x - 8x - 144

⇒ 0 = x(x + 18) - 8(x + 18)

⇒ 0 = (x + 18) (x - 8)

⇒ x = -18 (Not possible)

x = 8 cm

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