Galiya wrote:
Hi all!
Help me please with one task concerning inscribed triangles and circles
here it is:
Circle A,centre X. XB is the radius. There is a chord AC which intersects XB. D is the point of intersection between XB and AC. BD=2;AC=12;XDA= 90 degrees. What is the circles area?
By basic property of the circle,
the radius bisects the chord AC . ie CD equals AC/2 ie 6
now see, radius XB=XD+BD ie r=XD+2 ie XD=r-2
now concerning Triangle XCD, angle XDC= XDA =90 so pythagorean theorem is applicable
so, sq(XC)=sq(DC)+sq(XD)
plug in values you get sq(r)=sq(r-2)+sq(6)
which gives r=10
now area=pi*r*r=100*pi
Hope it helps.