You can't bash it out

Geometry Level 4

$P$ is a point on the base $BC$ of a $\triangle(ABC)$ and $r_{1},r_{2},r_{3}$ be the in-radii of the triangles $ABC,ACP,ABP$ respectively , $h_{a}$ is the length of altitude from $A$ to $BC$ . Find $h_{a}$ given that $r_{1}=5,r_{2}=3,r_{3}=4$ .

Bonus : Try to generalisze it.

The answer is 12.

1 solution

D G
Mar 21, 2016

You can bash anything if you're imaginative enough.

from math import *
import random

def dist(a, b):
    return sqrt((a[0]-b[0])**2 + (a[1] - b[1])**2)

def inradius(p1, p2, p3):
    a = dist(p1, p2)
    b = dist(p2, p3)
    c = dist(p1, p3)

    return sqrt((b+c-a)*(c+a-b)*(a+b-c)/(a+b+c))/2

record = 10**100

while True:
    a = random.uniform(0,30)
    b = random.uniform(0,30)
    c = random.uniform(0,30)
    d = random.uniform(0,a)

    B = [0,0]
    C = [a,0]
    A = [b,c]
    P = [d,0]

    r1 = inradius(A,B,C)
    r2 = inradius(A,C,P)
    r3 = inradius(A,B,P)

    test = (r1-5)**2 + (r2-3)**2 + (r3-4)**2
    if test < record:
        record = test
        print c

You can't bash it out

The answer is 12.

1 solution

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