SME
Grade 10 Math · Problem type
A tangent and its radius
Use this for “The radius is 8 and the tangent from P is 15. How far is P from the center?”
Diagram
A tangent meets the radius at a right angle, so OTP is a right triangle.
r² + t² = d²
8² + 15² = 17²
This is an example. Type your own values to start a new problem.
r
2
+
t
2
=
d
2
Formulas
r
2
+
t
2
=
d
2
8
2
+
15
2
=
17
2
Assumptions
•
A tangent touches the circle at one point T, at right angles to the radius OT.
•
So O, T and P make a right triangle with hypotenuse OP: r² + t² = d².
•
The two tangents from one point are equal in length.
Step-by-step
WE KNOW
r = 8, t = 15
FIND
distance OP (d)
Step 1 · Find distance OP (d)
Use r² + t² = d²
OP is the hypotenuse of the right triangle OTP.
d
=
√
r
2
+
t
2
d
=
√
8
2
+
15
2
d
=
√
64 + 225
d
=
√
289
d
=
17
Check
Put the numbers back in. Both sides should match.
8
2
+
15
2
=
17
2
✓
Topic check
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