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Question

If v is the circumcenter of pqr ,pr =46 ,tv=15,and vr=25 find each measure

Answer

1. a) SR = 23, b) QV = 25, c) QT = 20, d) PQ = 40, e) VS = 4·√6 2. a) LH = 16, b) EL = 2·√185, c) JG = 30, d) EK = 22, e) KG = 30 3. a) XT = 37, b) TZ = 34, c) ZW = 17, d) XZ = 21, e) SY = 69 Step-by-step explanation: 1. The circumcenter of ΔPQR is the center of the circle that circumscribes ΔPQR, and the length of the radius of the circle is equal to the length of VP, VR and QV. a) Using geometry and trigonometry, we can prove that SR is equal to half of PR (46), so SR = 23. b) Given that V is the center of the circle, the radius QV is 25. c) Using the Pythagorean theorem, we can find that QT is equal to 20. d) Using the fact that PQ is equal to the sum of QT and TP, and knowing that QT is equal to 20, we can calculate that PQ is equal to 40. e) Using the Pythagorean theorem, we can calculate that VS is equal to 4·√6. 2. The incenter of ΔEFG is the center of the incircle of ΔEFG. a) Since the incenter is equidistant from LH, LK, and LJ, and these line segments are all 16, we know that LH is equal to LK and LJ, and is therefore equal to 16. b) Using the Pythagorean theorem, we can calculate that EL is equal to 2·√185. c) Using the Pythagorean theorem, we can calculate that JG is equal to 30. d) Using the Pythagorean theorem, we can calculate that EK is equal to 22. e) Using the Pythagorean theorem, we can calculate that KG is equal to 30. 3. Point Z is the centroid of ΔRST. a) Since the centroid divides the median of ST in two equal parts, we know that XT is equal to XS, and therefore ST is equal to 2·XT, which is equal to 74. b) The length of TZ is two thirds of the length of TW, so TZ is equal to 2/3×TW, which is equal to 34. c) Using the fact that TZ + ZW is equal to TW, we can calculate that ZW is equal to 17. d) Using the fact that RZ is equal to 2/3×RX, and that RZ + XZ is equal to RX, we can calculate that XZ is equal to 21. e) Using the fact that SZ is equal to 2/3×SY, and that SZ + ZY is equal to SY, we can calculate that ZY is equal to 23. Since ZY is one third of SY, we know that SY is equal to 3×ZY, which is equal to 69.