Question

Find the Perimeter of the polygon if angle B= angle D Please Help Trying to graduate.

Answer 1

Answer:

P = 60 cm

Step-by-step explanation:

To solve this question we will use the property of the tangents drawn from a point to a circle.

"Length of tangents drawn from a point to a circle are equal in measure."

By this property,

Therefore, BG ≅ FB ≅ 7.5 cm

AG ≅ AH ≅ 6.5 cm

CF ≅ EC ≅ 8.5 cm

Since m∠B ≅ m∠D

Therefore, length of tangents FB ≅ GB ≅ DE ≅ DH ≅ 7.5 cm

Since, Perimeter of ABCD = AB + BC + CD + DA

AB = 7.5 + 6.5 = 14 cm

BC = 7.5 + 8.5 = 16 cm

CD = 8.5 + 7.5 = 16 cm

DA = 7.5 + 6.5 = 14 cm

Now Perimeter = 16 + 16 + 14 + 14 = 60 cm

Therefore, P = 60 cm will be the answer.