In the circle below, chord \(\overline {AB} \) is extended to meet the tangent \(\overline {DE}\) at D. If \(\overline {AB} \; = \;5\;cm\) and \(\overline {DE} \; = \;6\;cm,\) find the length of \(\overline {BD} \).

Question

Question

This question was previously asked in

RRB ALP Previous Paper 5 (Held On: 10 Aug 2018 Shift 3)

Answer 1

Concept Used:

10-Aug 3rd Shift Shraddha 20 - translated Reviewedc images Q2

According to the tangent secant theorem

DE2 = DB × DA

Calculation:

DB × DA = DE²

⇒ DB × (5 + DB) = 6²

⇒ DB × (5 + DB) = 36

⇒ 5DB + DB² = 36

⇒ DB² + 5DB - 36 = 0

Solving the above quadratic equation,

DB = (-9) or DB = 4

As length can't be negative, DB = 4 cm

∴ The length of DB is 4 cm.

Shortcut Trick

DB × (5 + DB) = 36

By checking the options, we can solve this equation in less time

Thus, Option 03 satisfies the equation

∴ The length of DB is 4 cm.

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