Mathematics
In the figure (i) given below, PAB is a secant and PT is tangent to a circle. If PA : AB = 1 : 3 and PT = 6 cm, find the length of PB.
Circles
ICSE
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Answer
Given, PA : AB = 1 : 3.
Let PA = k, so AB = 3k.
PB = PA + AB = k + 3k = 4k.
We know that,
If a chord and a tangent intersect externally, then the product of lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
∴ PT2 = PA × PB
⇒ 62 = k × 4k
⇒ 36 = 4k2
⇒ k2 =
⇒ k = cm
⇒ k = 3 cm.
PB = 4k = 4(3) = 12 cm.
Hence, the length of PB = 12 cm.
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