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1 (a). Find the inradius of triangle ABC.

1 (b). Find the circumradius of triangle ABC.

2. In triangle PQR, M is the midpoint of \(\overline{PQ}\). Let X be the point on \(\overline{QR}\) such that \(\overline{PX}\) bisects \(\angle QPR\) and let the perpendicular bisector of \(\overline{PQ}\). intersect \(\overline{PX}\) at Y. If PQ = 36, PR = 22, and MY = 8, then find the area of triangle PYR.

3 (a). In triangle ABC, let the angle bisectors be \(\overline{BY}\) and \(\overline{CZ}\). Given AB = 12, AY = 10, and CY = 8, find BC.

3 (b). In triangle ABC, let the angle bisectors be \(\overline{BY}\) and \(\overline{CZ}\). Given AB = 12, AY = 10, and CY = 8, find BZ.

 Jul 11, 2023
 #1
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1. (a)  Let s=(29+29+42)/2​=40. Then by Heron's formula, the area of triangle ABC is

[K = \sqrt{40(40 - 29)(40 - 29)(40 - 42)} = 420.]

The inradius is \frac{K}{s} = \frac{420}{40} = \frac{21}{2}.

 Jul 11, 2023
 #2
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jeeze, fella, (29+29+42)/2​ does NOT = 40  it's 50 

didnt you think something was wrong when you did 40-42  

Bosco  Jul 11, 2023
 #3
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Do not post A O P S problems.

 Jul 11, 2023
 #4
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youngwolf is just trying to cheat on homework.

 Jul 11, 2023
 #5
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We are not here to do all your homework for you, cheater.

 Jul 11, 2023

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