MathDB

3

Part of 2019 Stanford Mathematics Tournament

Problems(2)

SMT 2019 Geometry #3

Source:

8/8/2023
In triangle ABCABC with AB=10AB = 10, letD D be a point on side BC such that ADAD bisects ∠BAC\angle BAC. If CDBD=2\frac{CD}{BD} = 2 and the area of ABCABC is 5050, compute the value of ∠BAD\angle BAD in degrees.
geometry
SMT 2019 Geometry Tiebreaker #3 tangent circles

Source:

8/8/2023
Right triangle ABCABC with ∠ABC=90o\angle ABC = 90^o is inscribed in a circle ω1\omega_1 with radius 33. A circle ω2\omega_2 tangent to ABAB, BCBC, and ω1\omega_1 has radius 22. Compute the area of △ABC\vartriangle ABC.
geometry