Question

Chord ab is extended to meet tangent de at

d. If ab=5 and de=6 then find bd

Answer 1

Please find the attachment

Answer 2

Answer:

bd = 4 units

Step-by-step explanation:

For better understanding of the solution see the attached figure :

Let bd = x units ,

de = 6 units , ab = 5 units

⇒ ad = (x + 5) units

By using Secant Tangent theorem which states that : Product of the outside segment and whole secant equals the square of the tangent to the same point.

We get the following relation : de² = bd · ad

⇒ 6² = x · (x + 5)

⇒ 36 = x² + 5·x

⇒ x² + 5·x - 36 = 0

⇒ x² + 9·x - 4·x - 36 = 0

⇒ x·(x + 9) - 4·(x + 9) = 0

⇒ (x + 9)·(x -4) = 0

⇒ x = 4     or     x = -9

But distance cannot be negative so x = -9 is discarded.

So, x = 4

Hence, the length of bd is 4 units.