Question

Good luck!
A triangle AABC, right angled at C, is given. A semicircle is inscribed in
the triangle as shown on picture below. Express the length of the radius
using the lengths of the sides of triangle.
​

Answer 1

Answer:

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Step-by-step explanation:

ANSWER

AC is the diameter of he circle.

So, diameter AC extends a right angle on the circle.

So, measure of angle ABC is 90

o

.

So, in right △ ABC, AB

2

+ BC

2

= AC

2

Therefore, AC

2

= 8

2

+6

2

= 10

2

So, AC = 10 units.

AC is the diameter = 2 × the radius.

So, radius of given circle is 5 units.

Length of arc ABC = length of the semicircle = π R = 5π