Math Shortcut of the Day:
Topic: Circles
Agenda: How to find the radius of a circle given 2 intersecting chords which divide each other into segments a, b, c and d. Chords must be PERPENDICULAR to each other.
Example: Two chords of a circle intersect at a certain point. One chord has segments 4 cm and 6 cm. One segment of the other chord is 12 cm. Find the length of the radius of the circle.
Shortcut formula: 4r² = a² + b² + c² + d²
Solution:
As you can see, there is a missing segment. We will first use the Power of a Point (Intersecting Chord) to determine the other segment.
Concept: If two chords intersect in a circle and one chord has segments a and b while the other has segments c and d, the product of a and b is equal to the product of c and d. That is a x b = c x d :)
We have a = 4, b = 6, c = 12 and d is missing.
4(6) = 12d
d = 2
Then we will use the shortcut formula to determine the radius.
4r² = a² + b² + c² + d²
4r² = 4² + 6² + 12² + 2²
4r² = 16 + 36 + 144 + 4
4r² = 200
r² = 50
r = 5√2 cm :)
PS: This shortcut was derived using plane geometry :)
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-Engr. Isaiah James Maling, 2019-
