24) In the figure. Find the value of AB Where PT = 5cm and PA = 4cm.
T
5 cm
р
P
4 cm
A А
B
Answers
Answer:
Step-by-step explanation:
Let PA be x .
Information given:
We know PT = 6 cm
PA = x [ I assumed it as x ]
AB = 5 cm
From the figure is PB = PA + AB
==> PB = x + 5
Theorem
We know by properties of tangent that :
When a tangent and a chord meet externally or internally point then , the product of the line segments is equal to the square of the tangent!
This means that we can say :
PT² = PA × PB [ Using the above theorem ]
Length of PA
By using the formula :
(6)² = x (x+5)
==> x ( x + 5 ) = 36
==> x² + 5 x = 36
==> x² + 5 x - 36 = 0
==> x² + 9 x - 4 x - 36 = 0
==> x ( x + 9 ) - 4 ( x + 9 ) = 0
==> ( x - 4 )( x + 9) = 0
The value of x
The value of x is either x = 4 or x = -9
Well, we know the value of x cannot be negative as length cannot be negative.
So the value of x is 4.