MathDB

28

Part of 2019 India PRMO

Problems(2)

Geometry / Incicles and Incenters

Source:

8/11/2019
Let ABCABC be a triangle with sides 51,52,5351, 52, 53. Let Ω\Omega denote the incircle of △ABC\bigtriangleup ABC. Draw tangents to Ω\Omega which are parallel to the sides of ABCABC. Let r1,r2,r3r_1, r_2, r_3 be the inradii of the three corener triangles so formed, Find the largest integer that does not exceed r1+r2+r3r_1 + r_2 + r_3.
geometryincircleIncentersincenter
Computation Geo

Source: PRMO Leg 2 P28

8/25/2019
In a triangle ABCABC, it is known that ∠A=100∘\angle A=100^{\circ} and AB=ACAB=AC. The internal angle bisector BDBD has length 2020 units. Find the length of BCBC to the nearest integer, given that sin⁡10∘≈0.174\sin 10^{\circ} \approx 0.174
geometryPRMO