How to Calculate the Radius of the Circle ?

In this lesson, we demonstrated how to calculate the radius of the given circle. During our calculations, we utilized the Pythagorean theorem, the law of cosines, and the formula for calculating the area with sine. Later on, we used the relationship between the area of the triangle and the radius of the circle to find the length of the radius. To understand the steps of the process, please watch the video until the end. Enjoy watching!
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How to Calculate the Radius of the Circle ? :
• How to Calculate the R...
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A Nice Circle Problem - Can You Solve It ? :
• A Nice Circle Problem ...
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How to Find the Area of the Semi-Circle Easily:
• How to Find the Area o...
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Calculating the Shaded Area within the Semicircle | 2 Approaches
• Calculating the Shaded...
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How to Calculate the Area of the Right Triangle Inside a Semicircle:
• How to Calculate the A...
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How to Find the Area of the Triangle in the Semicircle ? | 2 Methods:
• How to Find the Area o...
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#circle #radius #maths

[@paricutin6320]

Nice problem. Thank You

[@RAG981]

When you get sin alpha =rt161/15, I think the sine rule formula 2R=12rt2/sin alpha is a simpler way to finish it off, don't you think?

[@johnspathonis1078]

Very interesting and challenging problem.. At time 2:48 you have two equations with two unknowns. At this point solve for C. Chord B-D becomes 5 times C. Now use intersecting chords theorum to find missing chord length. Once all chord lengths are known, use the formulae --- sum of each chord squared = 4 times R squared. Cheers

[@jimlocke9320]

That formula is only valid if the chords intersect at a right angle and you are referring to chord AC and the chord formed by extending BD. These chords intersect at D and not at a right angle. However, the formula can be used if BD and AE are extended into chords and we find the lengths to each side of point K, where the chords meet at a right angle. Extend BD into a chord and designate the second end point as M. Chord AC intersects chord MB. Use the intersecting chords theorem to compute length MD. Extend AE into a chord and designate the second end point as N. Chord BC intersects chord NA. Use the intersecting chords theorem to compute length EN. Now we have enough information to compute the segment lengths AK, BK, MK and NK on chords MB and NA, which do intersect at a right angle at point K. 4R² = (AK)² + (BK)² + (MK)² + (NK)². However, I must admit that I haven't done the math to confirm that this equation produces the same value of R that GeoMathry found.