Question

Question: Meghan has created a diagram of her city with her house, school, store, and gym identified. A. How far is it from the gym to the store? B. Meghan also wants to walk to get some exercise, rather than going to the gym. She decides to walk along arc AB. How far will she walk? Round to 3 decimal places.

Answer 1

a). Distance between the gym and store 9.25 m

b). Meghan will walk 5.637 m along the arc AB.

Explanation:

a). Theorem of intersecting chords inside the circle,

When two chords intersect each other in a circle multiplication of their segments are equal.

3×7 = 4a

a =
`(21)/(4)`

a = 5.25 m

Distance between the gym and store = 4 + 5.25

= 9.25 m

b). Length of an arc =
`(\theta)/(360)* (2\pi r)`

`\widehat{AB}` =
`(64.6)/(360)* 2\pi (5)`

=
`(646\pi )/(360)`

= 5.6374 m

≈ 5.637 m

Therefore, Meghan will walk 5.637 m along the arc AB.