Question

In right angle triangle two circles are placed which touch each other . If smaller circle has radius 2cm find thevradius of bigger circle.

Answer 1

Step-by-step explanation:

First draw figure as instructed

• a. triangleABC where angle B=90
• draw both circle like given in the Q
• centre of bigger circle =O'
• of smaller circle=O
• join O'to O and to C
• construct triangleCEO' angle C = 90 and it is point of contact of bigger circle and lie on hypotenuse of triangleABC
• NOW CONSTRUCT point of contact of smaller corcle=P
• make triangle CPO
• Po ll EO' in triangle CEO'
• SOLUTION

Let radius of bigger circle isEO'=rcm

angle PCO=30

IN TRIANGLE POC

sin30=PO/CO=1/2

CO=4cm

now CR=6cm henceCO'= 6+r cm

Now in triangle CEO'

sin30=1/2=EO/CO'

r/6+r=1/2(EO=r ,CO= 6+r)

2r=6+r

r=6cm

hence radius of bigger circle is 6cm

salute to sudhakar sir