Given 2concentric circles of radii a and b a>b find length of chord of larger circle which touches the other

Question

the other circle is smaller one

Answer 1

Theres Another method of doing this...

See, Let the diameter of the Bigger Circle and the Line touching the smaller circle be the two chord of the Bigger Circle.

Now we know that if two chord of a circle, AB and CD intesect each other at 'O' inside the circle, then: AO X OB = CO X OD (A theorm)

So applying this theorm here, we have:

Let the Half of the Lenght of Cord be 'k'


(a+b)(a-b) = k_sqr

a_sqr minus b_sqr = k_sqr

SqrRoot of [(a_sqr minus b_sqr)]= k

2 x [SqrRoot of {(a_sqr minus b_sqr)}]= 2k

Now 2k is what we have to find out i.e. "length of chord of larger circle which touches the other"

So, length of chord of larger circle which touches the other = 2 x [SqrRoot of {(a_sqr minus b_sqr)}]



Hence Solved...

Answer 2

When you say touches you mean is tangent to.

Draw the circles and the cord.

Because the cord is tangent to the smaller circle, it's radius can be drawn perpendicular to this cord. The radius of the larger circle can be drawn so that it intersects the same point where the cord intersects the larger circle. We now have a right triangle with leg b and hypotenuse a. 1/2 the length of the cord is therefore sqrt(a^2-b^2) and the full length of the cord is 2sqrt(a^2-b^2)

Answer 3

particular, certainly,the lines of centers proper a triangle (3,4,5). yet i do no longer comprehend your assertion that the slope of the line the place 2 circles meet is the comparable. of direction that's , because of the fact it rather is the comparable line. Nor do I see its relevance. the section you're speaking approximately is composed of arcs of the three circles. in case you connect the factors of tangency, you will style a triangle which incorporate chords of the three circles. in case you at the instant draw lines parallel to each chord and tangent to the corresponding circle, you will style yet yet another triangle. The circle inscribed for the period of this triangle stands out as the circle sought.

Answer 4

Dude try doing ur homework on ur own .All i can hint is pythagoras theorem.
Tangent perpend. to radius.
Perpend bisects the chord.