Question

please give me the answer for the 30 th one​

Answer 1

perimeter of shaded region = AB + BC + arc AC

Note : @ = angle theta

AB is the tangent to the circle and OA is radius...

Here OA is perpendicular to AB

=> AOB is a right angle triangle

=> cos @ = OA / OB = r / OB

=> cos @ = r / OB

=> OB = r / cos @ = r × sec @ ( 1 / cos @ = sec @ )

=> OB = r × sec @

Now OB = OC + BC = r + BC ( OC = radius = r )

=> OB = r + BC

=> r × sec @ = r + BC

=> BC = r × sec @ - r

Now in triangle AOB , we have

tan @ = AB / OA = AB / r

=> AB = r × tan@

Arc length AC =( @ / 360 ) × 2 × Pie × r

Thus , perimeter of shaded region

= AB + BC + arc AC

= r tan @ + r sec @ - r + ( @ / 360 ) × 2 × Pie × r

Answer 2

People are deleting my answer