Two concentric circles have radii 3 and 7 . Find, to the nearest hundredth, the length of a chor

step 1 So, we have two concentric circles. Concentric means the circle is having same center. So, let t

Two concentric circles have radii 3 and 7 . Find, to the...

Key Concepts

Pythagorean Theorem

The Pythagorean theorem is key in deducing the chord length formula. It relates the radius of the circle, the perpendicular distance from the center to the chord, and half the chord length, thereby forming a right triangle. This theorem is fundamental in establishing the relationship between these quantities in geometric problems.

Chord Length Calculation

The length of a chord in a circle can be calculated when you know the radius of the circle and the perpendicular distance from the center of the circle to the chord. This relationship is often expressed by the formula: chord length = 2?(R² - d²), where R is the radius of the circle and d is the distance from the center to the chord.

Concentric Circles

Concentric circles are circles that share the same center point but have different radii. This concept simplifies many geometric problems since the symmetry inherent in having a common center allows for easier calculation of distances and angles between the two circles.

Tangent to a Circle

A tangent to a circle is a line that touches the circle at exactly one point. In problems involving concentric circles, a chord of the larger circle being tangent to the smaller circle means that it just touches the smaller circle, leading to specific relationships between the chord's distance from the center and the radii of the circles.

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