Question

two circles with centres A and B of radius 3 cm and 4 cm respectively intersect at two points C and D such that AC and BC are tangents to the two circles. find the length of the common chord CD

Answer 1

HELLO DEAR,



GIVEN THAT:-

AC=3cm

,BC=4cm


IN∆ACB,<ACB=90°

(AB)²=(AC)²+(BC)²

(AB)²=9+16

(AB)=5cm






IN ∆ACP, <APC=90°


LET (CP)=Xcm

AND,

AP=Ycm


(CP)² +(AP)²= (AC)²

x²+y²=3²

x² = (9-y²)....-----------------(1)


IN∆BPC, <BPC=90°



BP=(5-y)


X²+(5-y)²=4²

x²=16-(5-y)²

x³=16-25-y²+10y


9-y²=-9-y²+10y


-y²+y²+9+9=10y

10y=18

y=1.8--------------(2)


x²={9-(1.8)²}

x²=9-3.24

x²=5.76


x=2.4cm


LENTH OF THE CHORDS CD=2×CP

=> 2×X.

CD=2×2.4 =4.8CM









I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

hope hope it helps u