Monday

January 26, 2015

January 26, 2015

Posted by **Hanna** on Sunday, December 4, 2011 at 6:53am.

- geometry -
**Reiny**, Sunday, December 4, 2011 at 9:52amJoin BD

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

= 450-450cosC

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**

**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 - In quadrilateral ABCD, we have AB = BC = CD = DA, AC = 14, and BD = ...

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...

geometry - in quadrilateral ABCD AC is a diagonol, m<ACD=2x+4 and m<ACB=5x...

geometry - Given quadrilateral ABCD, with A = 4x - 57 and C = x + 3, what value ...

geometry - ABCD is a quadrilateral with center O. AO=8, BO=11, CO=8, and DO=11. ...