+0  
 
0
184
4
avatar+965 

Let ABC be a triangle with\angle BAC = 90. A circle is tangent to the sides AB and AC at X and Y respectively, such that the points on the circle diametrically opposite X and Y both lie on the side BC. Given that AB = 6, find the area of the portion of the circle that lies outside the triangle.

 Aug 8, 2020
 #1
avatar+1421 
+3

Let the center of a circle be O and the midpoint of BC be M

 

Angle B = 45º

 

AM = sin( 45º) * 6

 

XY = 2/3 * AM            (Segment XY is a side of a square inscribed in a circle.)

 

Area of an inscribed square    As = XY2

 

r = sin(45º) * XY

 

Area of a circle     Ac = r2pi

 

Area of a shaded segment    A = (Ac - As) / 4 = pi - 2   smiley

 Aug 8, 2020
edited by Dragan  Aug 8, 2020
 #4
avatar
0

Awesome solution Dragan!!

Guest Aug 8, 2020
 #2
avatar+12484 
+1

Find the area of the portion of the circle that lies outside the triangle.

laugh

 Aug 8, 2020
edited by Omi67  Aug 8, 2020
 #3
avatar
0

Amazing solution Omi!!!!!
 

Guest Aug 8, 2020

39 Online Users

avatar
avatar
avatar
avatar