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Question
In the given figure, PT is a tangent to the circle with centre O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is ______.
Options
8 cm
10 cm
12 cm
16 cm
MCQ
Fill in the Blanks
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Solution
In the given figure, PT is a tangent to the circle with centre O. If OT = 6 cm and OP = 10 cm, then the length of tangent PT is 8 cm.
Explanation:
OT is the radius to the point of contact T, so OT ⟂ PT.
In right triangle OTP (right-angled at T),
`PT = sqrt(OP^2 - OT^2)`
= `sqrt(10^2 - 6^2)`
= `sqrt(100 - 36)`
= 8 cm
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