Showing posts with label Geometry Problems. Show all posts
Showing posts with label Geometry Problems. Show all posts
Problem 196. Triangle, Inradius and Exradii Formula
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Geometry Problems
In the figure below, given a triangle ABC, r is the inradius and ra, rb, rc, are the exradii. Prove that
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Problem 197. Area of a Triangle, Side, Inradius, and Exradius
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Geometry Problems
In the figure below, given a triangle ABC of area S, r is the inradius, and ra is the exradius relative to side BC = a. Prove that
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Problem 198. Triangle, Quadrilateral, Angles
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Geometry Problems
In the figure below, ABCD is a quadrilateral with AB = BD, the measure of the angles ACD and ACB are 50 and 65 degrees respectively. Find the measure of the angle ABD.
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Problem 199. Triangle, Altitude, Angles
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Geometry Problems
In the figure below, ABC is a triangle with the altitude BD. The measure of the angles ABD, DBC and BCE are 38, 68, and 14 degrees respectively. Find the measure of the angle CAE.
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Problem 200. Right Triangle, Incircle, Excircles, Points of Tangency, Inradius
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Geometry Problems
In the figure below, BAC is a right triangle with the incircle of radius r and the excircles relatives to the legs or catheti (singular: cathetus). If s is the semiperimeter and D, E, F, G, H, and M are the points of tangency, prove that r = s - a = AD = AE = BF = BH = CG = CM.
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