Question

The radii of two concentric circles are 13 and 8.A chord of the outer circle touches the inner circle. Find the length of that chord​

Answer 1

Answer:

R=13 cm

r= 8cm

The chord of the outer circle touching the inner circle is called the Tangent.

A Tangent of a circle is an external line touching the circle at a single point on the circle.

The radius of the inner circle is perpendicular to the circle due to the property of circles and their tangents, that is, Radius of a circle ⊥ Tangent.

The radius 8cm of the inner circle is perpendicular to the tangent at the point of contact.

The radius 13 cm of the outer circle is drawn to the point of the chord touching the circle.

A triangle is formed.

The hypotenuse is 13cm. The altitude or height is 8cm. The base is half the length of the chord (Radius ⊥ Tangent).

$Hypotenuse^{2}= Altitude^{2}+ Base^{2}$

$13^{2} =8^{2}+x^{2}$

$169=64+x^{2} \\169-64=x^{2} \\105=x^{2} \\\sqrt{105}= x$

The half of the chord is $\sqrt{105}$

The chord's length is 2$\sqrt{105}$

Step-by-step explanation:

Diagram, given below.