If and are the radi of two concentric circles and (r. > r.). If the chord of the larger circle AB touches the inter circle. Find the value of AB

r1 and r2 are the radii of two concentric circles

To find:

The length of the chord of the larger circle.

Solution:

We have given the two concentric circles which means both the circles have the same centre.

The chord of the larger circle toches the inner circle so the chord of the larger circle will be the tangent of the smaller circle.

And we know that the radius of the circle is perpendicular to the tangent of the circle.

Let 2x be the length of the chord of the circle.

r1 is the radius of the larger circle.

r2 is the radius of the smaller circle.

So by the Pythagoras theorem,

The length of the half of the chord is given by:

r1² = x² + r2²

x² = r1² - r2²

x = √r1² - r2²

So,

The length of the chord will be 2x = 2√r1² - r2² units

Step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.