C is the centre of two concentric circles. AB is a tangent to the smaller circle and a chord of the larger circle. The radius of the smaller circle is 6 cm. Chord AB = 16 cm. Calculate the radius of the larger circle.

Guest Nov 10, 2015

#2**+10 **

The radius of the larger circle = 10 cm

Here's a pic....

A radius drawn to a tangent meets that tangent at right angles. Thus, the radius of the smaller circle - OC - meets the tangent chord AB at right angles. And the radius of the larger circle meets the chord AB at right angles. And, by Euclid, a radius meeting a chord at right angles bisects that chord. So, triangle AOC is a 6 - 8 - 10 "Pythagorean Triple" right triangle with leg OC = 6 and leg AC = 8. And the hypotenuse - OA - equals the radius of the larger circle, i.e., 10 cm.

CPhill
Nov 10, 2015

#1**+10 **

ok

imagine that you draw a line from where the chord meets the larger circle to the centre - this is line A

the radius is line B

the chord - from point A to its midpoint is line C

ABC is a triange

BUT it is a right angled triangle

use pythagoras

side A = X

side B = 6

side C = 8

8squared + 6squared = xsquared = 100

x = 10

you will notice that this is also the radius of the larger circle!

ta dah!

hope this helped

Guest Nov 10, 2015

#2**+10 **

Best Answer

The radius of the larger circle = 10 cm

Here's a pic....

A radius drawn to a tangent meets that tangent at right angles. Thus, the radius of the smaller circle - OC - meets the tangent chord AB at right angles. And the radius of the larger circle meets the chord AB at right angles. And, by Euclid, a radius meeting a chord at right angles bisects that chord. So, triangle AOC is a 6 - 8 - 10 "Pythagorean Triple" right triangle with leg OC = 6 and leg AC = 8. And the hypotenuse - OA - equals the radius of the larger circle, i.e., 10 cm.

CPhill
Nov 10, 2015