Posted by Hanna on Sunday, December 4, 2011 at 6:53am.
quadrilateral ABCD has right angles at B and D. If ABCD is kite-shaped with AB=AD=20 and BC=CD=15, find the radius of the circle inscribed in ABCD.
- geometry - Reiny, Sunday, December 4, 2011 at 9:52am
BD will be a line of symmetry and the centre of the inscribed circle will have to be on AC and have to be the midpoint of BD. Let that point be P
BD^2 = 20^2 + 20^2 - 2(20)(20)cosA
= 800 - 800cosA
also BD^2 = 15^2+15^2-2(15)(15)cosC
so 450-450cosC= 800-800cosA
800cosA -450cosC = 350
but C = 180-A
cosC = cos(180-A) = -cosA
800cosA +450cosA = 350
CosA = .28 (nice)
A = 73.7398°
BD^2 = 800-800cosA = 800-800(.28) = 576
BD = √576 = 24
BP = 12
Let r be the radius of the circle from P to line AB
angle ABD = 53.13..°
and BP, the hypotenuse of that little triangle is
sin 53.13...° = r/12
r = 12sin53.13..° = 12(.8) = 9.6
Answer This Question
More Related Questions
- Geometry - ABCD is a trapezoid with AB < CD and AB parallel to CD. \Gamma is ...
- GEOmetry!!..... - ABCD is a trapezoid with AB<CD and AB parallel to CD. Γ...
- Geometry - The coordinates of the vertices of quadrilateral ABCD are A (-8, 8...
- Geometry - Circle O is inscribed is square ABCD, and at the same time, is ...
- geometry - If rectangle ABCD has vertices A(6, 2), B(2, 2), and C(0, 6), ...
- geometry - A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). ...
- Geometry - In quadrilateral ABCD, we have AB = BC = CD = DA, AC = 14, and BD = ...
- QUADRILATERAL MATHS - ABCD is a quadrilateral with angle ABC a right angle. The ...
- maths - Let ABCD be a square with side legnth 7cm. Another square KLMN is ...
- Geometry - ABCD is a quadrilateral inscribed in a circle with AB = 1, BC = 3, CD...