Question

Two circles have radii of 12 cm and 4 cm. If the length of a direct common tangent is 15 cm, what is the distance between their centers?

• A. 15 cm
• B. 17 cm
• C. 18 cm
• D. 20 cm

Answer 1

Answer:

B. 17 cm

For a direct common tangent, the relation is:

[
L^2 = d^2 - (R - r)^2
]

Where:

• (L = 15) cm (tangent length)

• (R = 12) cm

• (r = 4) cm

• (d) = distance between centers

---

Step 1: Substitute values

[
15^2 = d^2 - (12 - 4)^2
]

[
225 = d^2 - 8^2
]

[
225 = d^2 - 64
]

---

Step 2: Solve

[
d^2 = 225 + 64 = 289
]

[
d = \sqrt{289} = 17
]

---

✅ Final Answer:

[
\boxed{17 \text{ cm}}
]