Basic vs. Python: Circle Inscribed in Circle
Calculators Used:
Basic: HP 71B
Python: Casio fx-CG 100
Introduction
Let a rectangle with sides A and B be inscribed in a circle. The circle has a radius R. Let the line segments with the length A have a corresponding angle Θ. If we are given R and Θ, we can use the chord length formula to calculate A and B.
The angle corresponding with side B can be determined as:
φ: angle corresponding with side B
φ + Θ + φ + Θ = 360°
2 × (φ + Θ) = 360°
φ + Θ = 180°
φ = 180° - Θ
Chord length:
A = 2 × R × sin(Θ/2)
B = 2 × R × sin(φ/2) = 2 × R × sin((180° - Θ)/2)
Knowing A and B, we can calculate the following:
Area of the rectangle = A × B
Area of the shaded area (circle – rectangle) = π × R^2 – A × B
Basic: HP 71B – INSCRECT
10 DESTROY R,A,B,C,D,T
15 DEGREES @ FIX 5
20 DISP “RECT. INSCR. CIRCLE” @ PAUSED
25 DISP “DEGREES MODE” @ WAIT 0.5
30 INPUT “RADIUS? “; R
35 INPUT “ANGLE-SIDE A? “; A
50 A = 2 * R * SIN(T/2)
55 B = 2 * R * SIN((180 – T)/2)
60 C = A * B
65 D = R^2 * PI – C
80 DISP “SIDE A = “, A @ PAUSE
85 DISP “SIDE B = “, B @ PAUSE
90 DISP “RECT ANGLE = “, C @ PAUSE
95 DISP “CIRC-RECT = “, D @ PAUSE
98 STD
Notes:
* FIX 5: Fix 5 display
* STD: Standard mode, floating point display
* DEGREES: Sets the HP 71B in degrees mode
Python: Casio fx-CG 100, insecrect.py
from math import *
print(“Rectangle Inscribed in a Circle”)
print(“Math module imported”)
r=eval(input(“Radius? “))
print(“Enter angle in degrees”)
t=eval(input(“Angle- A? “))
u=t*pi/180
a=2*r*sin(u/2)
b=2*r*sin((pi-u)/2)
c=a*b
d=r**2*pi-c
print(“A: {0.5f}”.format(a))
print(“B: {0.5f}”.format(b))
print(“Rect. Area: {0.5f}”.format(c))
print(“CIRC-AREA: {0:.5f}”.format(d))
Notes:
* Since the math module is used, this script can be used in any calculator with Python.
* Python’s angle mode is always in radians.
Examples
Example 1:
Inputs:
r = 10
Θ = 30°
Outputs:
a ≈ 5.17638
b ≈ 19.31852
c = 100
d ≈ 214.15927
Example 2:
Inputs:
r = 20
Θ = 80°
Outputs:
a ≈ 25.71150
b ≈ 30.64178
c ≈ 787.84620
d ≈ 468.79086
Example 3:
Inputs:
r = 20
Θ = 90°
Outputs:
a ≈ 35.35534
b ≈ 35.35534
c = 1250
d ≈ 713.49541
Eddie
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