Sagot :
There are two ways to find the radius of circumscribing circle of a triangle (triangle inside the circle and whose three vertices are on the circle).
Choose one that you can easily remember:
Method A:
1.) Find the semi-perimeter (s) of the triangle, where a, b, and c are the sides
of the triangle:
s = (a + b+ c) ÷ 2
2.) Solve for the radius (r) given the semi-perimeter (s) of the triangle, and the
the sides a, b, and c:
r = [tex] \frac{abc}{4 \sqrt{s(s-a)(s-b)(s-c)} } [/tex]
Solution using Method A:
a = 80 cm; b = 100 cm; c = 140 cm
Find the triangle's semi-perimeter: (half of the triangle's perimeter)
s = (80 + 100 + 140) ÷ 2
s = 320 cm ÷ 2
s = 160 cm
Solve for radius given the semi-perimeter (160 cm) and sides a, b, c:
r = (abc) ÷ [tex]4 \sqrt{s(s-a)(s-b)(s-c)} [/tex]
r = [tex] \frac{(80cm)(100cm)(140cm)}{4 \sqrt{140cm(160cm-80cm)(160cm-100cm)(160cm-140cm)} } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{4 \sqrt{(160cm)(80cm)(60cm)(20cm)} } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{4 \sqrt{15,360,000cm ^{4} } } [/tex]
r =[tex] \frac{1,120,000cm ^{3} }{4 (3,919.18cm ^{2}) } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{15,676.72cm ^{2} } [/tex]
r ≈ 71.44 cm
ANSWER: The radius of circumscribing circle is 71.44 cm.
Method B:
r = [tex] \frac{abc}{ \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-a)} } [/tex]
Substitute the given measurements of sides a, b and, c, then evaluate.
The result is the same.
Choose one that you can easily remember:
Method A:
1.) Find the semi-perimeter (s) of the triangle, where a, b, and c are the sides
of the triangle:
s = (a + b+ c) ÷ 2
2.) Solve for the radius (r) given the semi-perimeter (s) of the triangle, and the
the sides a, b, and c:
r = [tex] \frac{abc}{4 \sqrt{s(s-a)(s-b)(s-c)} } [/tex]
Solution using Method A:
a = 80 cm; b = 100 cm; c = 140 cm
Find the triangle's semi-perimeter: (half of the triangle's perimeter)
s = (80 + 100 + 140) ÷ 2
s = 320 cm ÷ 2
s = 160 cm
Solve for radius given the semi-perimeter (160 cm) and sides a, b, c:
r = (abc) ÷ [tex]4 \sqrt{s(s-a)(s-b)(s-c)} [/tex]
r = [tex] \frac{(80cm)(100cm)(140cm)}{4 \sqrt{140cm(160cm-80cm)(160cm-100cm)(160cm-140cm)} } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{4 \sqrt{(160cm)(80cm)(60cm)(20cm)} } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{4 \sqrt{15,360,000cm ^{4} } } [/tex]
r =[tex] \frac{1,120,000cm ^{3} }{4 (3,919.18cm ^{2}) } [/tex]
r = [tex] \frac{1,120,000cm ^{3} }{15,676.72cm ^{2} } [/tex]
r ≈ 71.44 cm
ANSWER: The radius of circumscribing circle is 71.44 cm.
Method B:
r = [tex] \frac{abc}{ \sqrt{(a+b+c)(b+c-a)(c+a-b)(a+b-a)} } [/tex]
Substitute the given measurements of sides a, b and, c, then evaluate.
The result is the same.