a poor artist on the street makes funny cartoons for children to earn his living once he made a comic - Maths - Areas Related to Circles

Question

​​​a
poor artist on the street makes funny cartoons for children to earn
his living once he made a comic face by drawing a circle within a
circle the radu=ius of the bigger circle being 30 cm and that of
smaller circle bbeing 20 cm a shown in picture what is area of cap
?????????????

plz tell fast
if you like question plz like
​Thank You

Ishwarmani · Accepted Answer

Dear
Student,
Please find
below the solution to the asked query:

<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_56ec05713be6c%20png"
style="width: 403px; height: 408px;">
Let A and B be the centres of the smaller and bigger circles,respectively
We have,BC=BD=BF=BE=30 cm,AP=AF=20 cmar∆CDE=?Let ∆CDE be an isosceles triangle representing the capAs, BF=30 cm⇒AB+AF=30⇒AB+20=30⇒AB=30-20=10 cmSo, BP=AP-AB=20-10=10 cm        
iAlso, BE=30 cm⇒BP+PE=30⇒10+PE=30⇒PE=30-10⇒PE=20 cm       
iiSince, CD is a tangent to the smaller circleSo, BP⊥CD          Tangent is perpendicular to the radius at the point of contactAlso, CD is a chord of the bigger circleSo, CP=DP          Perpendicular drawn from centre to the chord bisects the chord      
iiiNow, in ∆BPC, using pythagoras theoremCP2=BC2-BP2⇒CP=302-102          As, BC=30 cm, given and BP=10 cm, from i⇒CP=900-100=800⇒CP=202 cmSo, CD=2CD               From iii⇒CD=2202=402 cmNow, ar∆CED=12×CD×PE=12×402×20⇒ar∆CED=4002 cm2Hence, the area of the cap is 4002 cm2

Hope
this
information will clear
your doubts about the
topic

If you have
any more doubts just ask here on the forum and our experts
will
try to help
you out as soon as possible
Regards