# mathematics

an isosceles triangle ABC has its vertices on a circle.if /AB/=13CM,/BC/=13cm and /AC/=10CM,calculate the radius of the circle,to nearest whole cm

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1. from diagram
sin=5/13=0.3846
=22.6
now angle at center is twice the angle at any point of the circumference
22.6*2=45.2
sin45.2=5/r
now find r

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2. Place the circle in such a way that the midpoint of CA becomes the origin, and
B lies on the y-axis
by Pythagoras BO = 12 cm
so we have points A(5,0), B(0,12) and C(-5,0)
let the centre be (0,k) and the radius r
equation:
x^2 + (y-k)^2 = r^2

using (5,0) --> 25 + k^2 = r^2
using (0,12) -> 0 + (12-k)^2 = r^2
12-k = r
k = 12-r

in 25+k^2 = r^2
25 + (12-r)^2 = r^2
25 + 144 - 24r + r^2 = r^2
24r = 169
r = 169/24 = 7.04166

The radius is appr 7 cm

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3. It is correct and good

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4. Yes

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5. Thanks but i mean using diagram

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6. Explain it with diagram pls

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