Question

Two concentric circles of diameter 30 cm and 18cm find the length of the chord of the larger circle that touches the smaller circle

Answer 1

Answer

The length of the chord of the larger circle that touches the smaller circle is 30cm or less than 30cm

Solution

From the figure  attached with this answer shows two circles

Larger circle with diameter 30cm and smaller circle with diameter 18cm

The smaller circle just touches the larger circle.From that point diameter is one of larger chord of the circle.

So we can draw many number of chord in the larger circle that just touches the smaller circle, Then the length of chords less than 30cm.

Answer 2

Since the chord of the larger circle touches the smaller circle, Hence it becomes a tangent to the smaller circle.

We know that the tangent touches a circle at perpendicular to the radius.

Hence half of the chord, radius of the larger circle and radius of the smaller circle makes a right angle triangle,

Hence ,for right angle triangle

h² = p²+b²

=> 15² = 9² + b²

=> b² = 225-81 = 144

=> b = 12 cm

Hence the total length of the chord = 2 x 12 = 24 cm