Basic vs. Python: Circle Inscribed in Circle [HP 71B, Casio fx-CG 100]

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

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.

HP 71B Programs: September 2025

HP 71B Programs: September 2025

One of my favorite calculators/pocket calculators of all time is the HP 71B.

ADDMOD: (a + b) mod n = a mod n + b mod n

10 DESTROY A, B, N

20 DISP “(A+B) MOD N” @ WAIT .5

30 INPUT “A? “; A

40 INPUT “B? “; B

50 INPUT “C? “; C

60 S = MOD(A, N) + MOD(B, N)

70 S = MOD(S, N)

80 DISP “SUM = “; S

MULTMOD: (a * b) mod n = a mod n * b mod n

10 DESTROY A, B, N

20 DISP “(A*B) MOD N” @ WAIT .5

30 INPUT “A? “; A

40 INPUT “B? “; B

50 INPUT “N? “; N

60 P = MOD(A, N) * MOD(B, N)

70 P = MOD(P, N)

80 DISP “PRODUCT = “; P

Examples:

A	630	48	15
B	320	99	47
N	700	15	7
SUM:	250	12	6
PRODUCT:	0	12	5

GABLE: Area of a Gable Roof

10 DESTROY P, S, L

20 DEGREES

30 INPUT “PITCH (IN.)? “; P

40 INPUT “SPAN (FT.)? “; S

50 INPUT “LENGTH (FT.)? “; L

60 A = 2 * S * L / COS(ATAN(P/12))

70 DISP “AREA = “; A; “ FT^2”

Input: Pitch (P)	6”	3”	4”
Input: Span (S)	110” (110/12 ft)	5’ 8” (5 + 8/12 ft)	15 ft
Input: Length (L)	100” (100/12 ft)	10’	10 ft
Output: Area (A)	170.81074828 ft^2	116.821326059 ft^2	316.227766017 ft^2

INTENSE: Light Intensity of a Spherical or a Cylindrical Light Source

intensity = power / surface area

intensity (W/m^2), power (W), surface area (m^2)

Surface area: sphere = 4 * π * r^2, cylinder = 2 * π * (r * h + r^2)

10 DESTROY P, K$, R, H

20 DISP “INTENSITY OF LIGHT!” @ WAIT .5

30 INPUT “POWER (W)? “; P

40 DISP “1. SPHERE 2. CYLINDER”

50 DELAY 0,0

60 K$ = KEY$

70 IF K$ = “1” OR K$ = “S” THEN GOTO 100

80 IF K$ = “2” OR K$ = “C” THEN GOTO 200

90 GOTO 40

100 INPUT “RADIUS (M)? “; R

110 A = 4 * PI * R^2

120 GOTO 300

200 INPUT “RADIUS (M)? “; R

210 INPUT “HEIGHT (M)? “; H

220 A = 2 * PI * (R * H + R^2)

230 GOTO 300

300 I = P / A

310 DISP I; “W/M^2”

Examples:

Sphere: r = 4 m, Power = 60 W: Intensity = .298415518297 W/M^2

Cylinder: r = 1.25 m, h = 0.75 m, Power = 70 W; Intensity = 4.45633840656 W/M^2

SIMPLE: Simple Interest – Banker’s Rule

interest = amount * rate% / 100 * #days / 360

final = principal + interest (final, maturity value)

10 DESTROY P, R, I, M

20 DISP “SIMPLE INTEREST” @ WAIT .5

30 INPUT “AMT? “; P

40 INPUT “RATE%? “; R

50 INPUT “# DAYS? “; D

60 I = P * R * D / 360 / 100

70 M = P + I

80 IMAGE K, M10D.2D

90 DISP USING 80; “INT.=”, I @ PAUSE

100 DISP USING 80; “FINAL=”, M

Notes:

* When the HP 71B is in pause, press [ f ] [ + ] to continue (CONT).

* To stop execution, press [ ON ] (ATTN).

* IMAGE K, M10D.2D: display “prompt string”, number rounded to 2 decimal places. The number is right-justified, make the prompt string 7 characters or less to fit both the string and number on the screen.

Examples

Input: Amount	1500	2000	2800
Input: Rate %	4.00%	8.00%	6.65%
Input: # Days	180	90	60
Output: Interest	30	40	31.03
Output: Final	1530	2040	2831.03

AIRSOUND: Speed of Sound in Air

S = 331.5 + .606 * T

S = speed of sound in air, m/s

T = temperature in °C

10 DESTROY K$, S, T

20 DISP “SPEED OF SOUND IN AIR” @ WAIT .5

30 DISP “SOLVE FOR…” @ WAIT .5

40 DISP “1. SPEED 2. TEMP”

60 K$ = KEY$

70 IF K$=”1” OR K$=”S” THEN GOTO 100

80 IF K$=”2” OR K$=”T” THEN GOTO 200

90 GOTO 40

100 INPUT “TEMP (°C)? “; T

110 S = 331.5 + .606 * T

120 DISP “S=”; S; “ M/S”

130 END

200 INPUT “SPEED (M/S)? “; S

210 T = (S- 331.5) / .606

220 DISP “T=”; T ; “°C”

230 END

Examples:

Input: T = 74 °F = (32 + 1/3) °C Output: S = 345.64 m/s	Input: S = 350 m/s Output: T = 30.5280528053 °C
Input: T = -8.5 °C Output: S = 326.349 m/s	Input: S = 382 m/s Output: T = 83.3333333333 °C

Eddie

All original content copyright, © 2011-2025. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.

The author does not use AI engines and never will.