MathDB

2

Part of 2014 Stanford Mathematics Tournament

Problems(2)

SMT RMT 2014 Geometry #2

Source:

10/28/2022
In a circle, chord ABAB has length 55 and chord ACAC has length 77. Arc ACAC is twice the length of arc ABAB, and both arcs have degree less than 180180. Compute the area of the circle.
geometry
SMT RMT 2014 Geometry Tiebreaker #2

Source:

10/28/2022
Let ABCABC be a triangle with sides AB=19AB = 19, BC=21BC = 21 and AC=20AC = 20. Let ω\omega be the incircle of ABCABC with center II. Extend BIBI so that it intersects ACAC at EE. If ω\omega is tangent to ACAC at the point DD, then find the length of DEDE.
geometry