Question:
PT is a tangent and PAB is a secant , If PT=6cm and AB=5cm,find the length of PA
Answer:
Given, PT is a tangent and PAB is a secant.
Again given, PT = 6 cm and AB = 5 cm
Acoording to the secant property of the circle,
PT2 = PA * PB ..........1
=> 62 = PA * PB
=> 36 = PA * PB
Also, PB = PA + AB
=> PB = PA + 5 ........2
From equation 1, we get
=> 36 = PA * (PA + 5)
=> 36 = PA2 + 5PA
=> PA2 + 5PA - 36 = 0
=> PA2 + 9PA - 4PA - 36 = 0
=> PA(PA + 9) - 4(PA + 9) = 0
=> (PA + 9) * (PA - 4) = 0
=> PA = 4, -9
Since length can not be negative,
So, PA = 4 cm
Hence, the length of PA is 4 cm
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