Geometric Art: Typography, iPad

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## Saturday, August 4, 2018

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## Saturday, August 4, 2018

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Typography of Geometry Problem 1373: Isosceles Triangle, Exterior Cevian, Inradius, Exradius, Altitude, iPad Apps

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altitude,
circle,
geometric art,
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isosceles,
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Let the in circle be P and the excircle be Q

ReplyDeleteLet DAC touch circle P at X & circle Q at Y

Let DB touch circle P at U and circle Q at V

Let AB = BC = a, AX = b, CY = c and

AE = EC = d

Let the bisector of < BAE meet BE at T

ET = hd / (a + d) ......(1)

Now PXA, TEA & QYC are similar triangles

So b / r1 = c / r2 = ET / d = h / (a + d)

= (b + c) / ( r1 + r2) = (a - d) / (r1 + r2) from (1)

Hence (r1 + r2)h = a^2 - d^2 = h^2

Therefore r1 + r2 = h

Sumith Peiris

Moratuwa

Sri Lanka