A circle has radius of 18 cm. Find the area of the smaller of the two regions determined by a chord with length of 18√2 cm . Hin

Question

UkoKoshka [18]

2 years ago

7

A circle has radius of 18 cm. Find the area of the smaller of the two regions determined by a chord with length of 18√2 cm . Hin

t: (Look for right triangles using Pythagorean Theorem Converse)

Mathematics

2 answers:

boyakko [2] · Answer 1 · 2022-09-03T07:06:24+03:00

The area is 81*pi-162. Look at the triangle formed by the chord and the two radii connected to the endpoints of the chord. Since 18^2+18^2=(18*\sqrt2)^2, this is an isosceles right triangle by Pythagorean theorem. The area of the quarter circle containing the region we look for is pi*18^2/4=81*pi. The area of the right triangle is 18*18/2=162. The difference between these two areas, or 81*pi-162, is the area of the smaller region.

madreJ [45] · Answer 2 · 2022-09-03T08:28:22+03:00

madreJ [45]2 years ago

3 0

Answer:

81pi - 162

Step-by-step explanation: