consider a square ABCD of side 60cm It contains arcs BD and AC drawn with centres at A - Maths - Circles

Question

consider a square ABCD of side 60cm It contains arcs BD and AC
drawn with centres at A and Drespectively A circle is drawn such
that it is tangent to side AB with arcs BD and AC What is the
radius of the circle?

Utsav · Accepted Answer

Now as we know that when two circles touches each other internally
then distance between their centres is the difference of their
radiiand when they touch each other externally then distance
between their centre is sum of their radiiLet the required radius
of the circle be r cmHence AO= (60-r) and DO =(60+r)Now QO2=AP2And
AP2=AO2-OP2(using pythagoras theorem)Hence QO2= (60-r)2-r2 (1)Now
in ∆DQO , we haveQO2=DO2-DQ2 (using pythagoras
theorem)⇒(60-r)2-r2=(60+r)2-(60-r)2⇒3600+r2-120r-r2=3600+r2+120r-3600-r2+120r⇒360r
=3600⇒r=10 Hence the radius of the circle is 10 cm

consider a square ABCD of side 60cm . It contains arcs BD and AC drawn with centres at A and Drespectively. A circle is drawn such that it is tangent to side AB with arcs BD and AC.What is the radius of the circle?