Points P and Q are on AB of right triangle ABC, PB=CB, AQ=AC. If the diameter of the inscribed circle is 10, what is the diameter of the circumscribed circle of PCQ?
2007-02-23 16:01:58 · 3 answers · asked by need help! 3 in Science & Mathematics ➔ Mathematics
and of course - explain! thanks ahead of time :)
2007-02-23 16:12:58 · update #1
If the diameter of the inscribed circle is 10, then the diameter of the circumscribed circle is 10√2.
To understand why, the lines from A, B, and C to the center of the inscribed circle bisects angles BAC, CBA, and ACB. From this fact, lines from P, Q, and C to the center of the inscribed circle are all of equal lengths, which is the radius of the circumscribed circle. Therefore, it's easily shown that this radius is √2. times longer than the radius of the inscribed circle.
2007-02-23 18:15:53 · answer #1 · answered by Scythian1950 7 · 1⤊ 0⤋
you're stepped ahead (I considered your solutions) Use Heron's formula for section and use perimeter like a million/2 sum of roots = 8 sum of double product 80 one and made up of three root like 128 once you locate portion of triangle then r (a+b+c)=2S !!! and also you locate radius of inscribed circle. For R ( circumscribed ) use 2R = abc/(2S) a+b+c = 16 ab+ac+bc=80 one abc=128 do not sparkling up the equipment you comprehend!!! write expresion utilizing in effortless words sum and/or product
2016-12-04 21:09:18 · answer #2 · answered by ? 4 · 0⤊ 0⤋
should be 20
2007-02-23 16:11:50 · answer #3 · answered by alpha 7 · 0⤊ 0⤋