Question

Find if line M is a tangent line to circle B.

Answer 1

No

Explanation:

The tangent line must form a right angle with the radius

No, 4 5 6 isn't a right triangle

Answer 2

Line m is not a tangent line to circle B.

Explanation:

The tangent line to a circle is always perpendicular to the radius.

The line segment measuring 4 units is the radius of Circle B, therefore if line m is a tangent line to the circle, the angle between this segment and the segment measuring 5 units will be a right angle (90°).

We can use Pythagoras' Theorem to check if the triangle is a right triangle.

Pythagoras’ Theorem:
`a^2+b^2=c^2`

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Therefore, the legs are the line segments measuring 4 and 5, and the hypotenuse is the line segment measuring 6 units.

Substituting the values for the legs into the formula:

`\implies 4^2+5^2=c^2`

`\implies 16+25=c^2`

`\implies 41=c^2`

`\implies c=√(41)`

Therefore, as the hypotenuse of the triangle is not √41, the triangle is not a right triangle, and therefore line m is not a tangent line to circle B.