Question

The sides of ∠A are tangent to circle k(O) with radius r. Find: r, if OA=14 dm, m∠A=90°.

Answer 1

Explanation:

Alright, lets get started.

Please refer the diagram I have attached.

The angle A is 90 degree.

The side OA is 14.

There will be a right triangle formed.

So, Using Pythagorean theorem,

`r^2+r^2=14^2`

`2r^2=196`

Dividing 2 in both sides

`r^2=(196)/(2)=98`

`r=√(98)`

`r=7√(2)`

So,the answer is
`7√(2)` : Answer

Hope it will help :)

Answer 2

r = √98

Explanation:

angle A and the diameter form an isosceles right triangle, with OA as the hypotenuse and r as the other sides. You can then make and solve an equation from the Pythagorean Theorem:

r^2 + r^2 = 14^2

2r^2 = 14^2

2r^2 = 196

r^2 = 98

r = √98