Question

⦿(0, r₁) and ⦿(0, r₂) are such that rı > r2. Chord AB of ⦿(0, r₁) touches (0, r₂). Find AB in terms of r₁, and r₂.

Answer 1

According to the problem given ,

OB = r1

OP = r2

Chord AB of large circle is tangent

to smaller circle .

OP perpendicular bisector of AB

In ∆OBP , we have

OB² = OP² + BP²

r1² = r2² + BP²

BP² = r1² - r2²

BP = √ r1² - r2²

AB = 2BP

= 2√( r1² - r2²

I hope this helps you.

: )