MathDB

9

Part of 2009 Hanoi Open Mathematics Competitions

Problems(2)

another area computational, BR = RS = SC (2009 HOMC Junior Q9)

Source:

7/18/2019
Let be given △ABC \vartriangle ABC with area (△ABC)=60 (\vartriangle ABC) = 60 cm2^2. Let R,SR,S lie in BCBC such that BR=RS=SCBR = RS = SC and P,QP,Q be midpoints of ABAB and ACAC, respectively. Suppose that PSPS intersects QRQR at TT. Evaluate area (△PQT)(\vartriangle PQT).
geometryarea of a triangleareas
T= (BCA')^2+ (BCA')^2+ (ABC')^2, sum of areas, (HOMC 2009 Q9)

Source:

7/25/2019
Give an acute-angled triangle ABCABC with area SS, let points A′,B′,C′A',B',C' be located as follows: A′A' is the point where altitude from AA on BCBC meets the outwards facing semicirle drawn on BXBX as diameter.Points B′,C′B',C' are located similarly. Evaluate the sum T=(T=(area △BCA′)2+(\vartriangle BCA')^2+(area △CAB′)2+(\vartriangle CAB')^2+(area △ABC′)2\vartriangle ABC')^2.
geometryarea of a triangleareas