SME
Grade 10 Math · Problem type
Two secants from a point
Use this for “From P, PA = 3 and PB = 10 on one secant, PC = 5 on the other. Find PD.”
Diagram
Two secants from P: outside part × whole secant is the same for both.
Products: PA × PB = PC × PD
3 × 10 = 5 × 6 = 30
This is an example. Type your own values to start a new problem.
PA
×
PB
=
PC
×
PD
Formulas
PA × PB = PC × PD
3 × 10 = 5 × 6
Assumptions
•
Two secants from P outside the circle: PA and PC are the outside parts, PB and PD the whole secants.
•
Outside part × whole secant is the same for both: PA × PB = PC × PD.
•
The whole secant is the outside part plus the part inside: PB = PA + AB.
Step-by-step
WE KNOW
PA = 3, PB = 10, PC = 5
FIND
PD (whole) (PD)
Step 1 · Find PD (whole): PD
Use PA × PB = PC × PD
Two secants from one point: outside part × whole secant is equal.
PD
=
PA
×
PB
PC
PD
=
3
×
10
5
PD
=
30
5
PD = 6
Check
Put the numbers back in. Both sides should match.
3 × 10 = 5 × 6 ✓
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