Mathematics
In the figure (i) given below, PT is a tangent to the circle. Find TP if AT = 16 cm and AB = 12 cm.
Circles
ICSE
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Answer
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.
∴ TP2 = AT × BT
From figure,
BT = AT - AB = 16 - 12 = 4 cm.
Putting values we get,
⇒ TP2 = 16 × 4
⇒ TP2 = 64
⇒ TP =
⇒ TP = 8 cm.
Hence, the length of TP = 8 cm.
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