SME
Grade 10 Math · Problem type
A tangent and a secant from a point
Use this for “From P, PA = 4 and PB = 16 on a secant. How long is the tangent PT?”
Diagram
A tangent and a secant from P: the tangent squared is outside part × whole secant.
Tangent squared: PT² = PA × PB
8² = 4 × 16 = 64
This is an example. Type your own values to start a new problem.
PT
2
=
PA
×
PB
Formulas
PT² = PA × PB
8
2
=
4
×
16
Assumptions
•
From P, a tangent touches the circle at T and a secant crosses it at A and B.
•
The tangent squared is outside part × whole secant: PT² = PA × PB.
•
The whole secant is the outside part plus the part inside: PB = PA + AB.
Step-by-step
WE KNOW
PA = 4, PB = 16
FIND
PT (tangent) (PT)
Step 1 · Find PT (tangent): PT
Use PT² = PA × PB
The tangent is the square root of outside part × whole secant.
PT
=
√
PA × PB
PT
=
√
4 × 16
PT
=
√
64
PT = 8
Check
Put the numbers back in. Both sides should match.
8
2
=
4
×
16
✓
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