MathDB

12

Part of 2022 BMT

Problems(2)

BMT 2022 Guts #12

Source:

8/31/2023
Let circles C1C_1 and C2C_2 be internally tangent at point PP, with C1C_1 being the smaller circle. Consider a line passing through PP which intersects C1C_1 at QQ and C2C_2 at RR. Let the line tangent to C2C_2 at RR and the line perpendicular to PR‾\overline{PR} passing through QQ intersect at a point SS outside both circles. Given that SR=5SR = 5, RQ=3RQ = 3, and QP=2QP = 2, compute the radius of C2C_2.
geometry
BMT 2022 General p12

Source:

9/28/2023
Parallelograms ABGFABGF, CDGBCDGB and EFGDEFGD are drawn so that ABCDEFABCDEF is a convex hexagon, as shown. If ∠ABG=53o\angle ABG = 53^o and ∠CDG=56o\angle CDG = 56^o, what is the measure of ∠EFG\angle EFG, in degrees? https://cdn.artofproblemsolving.com/attachments/9/f/79d163662e02bc40d2636a76b73f632e59d584.png
geometry