Question

If a,b (b is greater than a) be the diameter of two concentric circles and c be the length of chord of a circle which is tangent to the other circles,then find the value of b in terms of a and c

Answer 1

Solution:

It is given that a, b are diameter of two concentric circles.

So,let me define first meaning of concentric circles. Circles are said to be concentric if they have same center.

Radius of circles will be $\frac{a}{2},\frac{b}{2},$.

As, given , b>a.

And c is the tangent to circle having diameter a.

Draw ⊥ from circle having diameter a to the chord c.

As you must keep in mind , ⊥ from center to chord bisects to chord.

AM= MB= $\frac{c}{2}$

In Right Δ O AM

Using Pythagoras theorem

OM²+AM²= OA²

$[\frac{a}{2}]^2+[\frac{c}{2}]^2=[\frac{b}{2}]^2\\\\a^2 +c^2=b^2\\\\ b=\sqrt{c^2+a^2}$