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I need some help on this question please! It says... Points B and D are points of...
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If B and D are tangents then line BC is perpendicular to AB. Similarly CD is perpendicular to AD.
Then triangle ABC and ADC become right triangles.
For both triangles AC is the hypotenuse. BC and CD are radius of the circle.
By Pythagoras theorem;
`AC^2 = AB^2+BC^2`
`AC^2 = AD^2+CD^2`
`AD^2+CD^2 = AB^2+BC^2`
But `BC = CD` (radius of circle)
`AD^2 = AB^2`
`AD = AB`
`x+10 = x^2+x-6`
`x^2 = 16`
`x = +-4`
When x = 4
`AB = x^2+x-6 = 16+4-6 = 14`
When x = -4
`AB = x^2+x-6 = (-4)^2-4-6 = 6`
So the possible length of AB is 14 and 6.
Posted by jeew-m on June 5, 2013 at 10:09 AM (Answer #1)
High School Teacher
Best answer as selected by question asker.
A tangents to a circle from an exterior point are equal in length.
Thus possible length of two tangents are 14 or 6
Posted by aruv on June 5, 2013 at 10:14 AM (Answer #2)
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