Circle
Tangent Circles
Premium Question
Grade 11
Question:
Two circles, each of radius 5, touch each other at $(1, 2)$. If the equation of their common tangent at the point of contact is $4x + 3y = 10$, the distance between their centres is:
(1) $5$
(2) $10$
(3) $2\sqrt{5}$
(4) $4\sqrt{5}$
Step-by-Step Solution
Key Concept: The circles touch each other, so the distance between centres equals the sum of radii (external contact) or the difference (internal). Since both radii equal 5 and they are distinct circles touching at one point, they touch externally: $d = 5 + 5 = 10$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)