Question

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Please help me with 34

Is AB tangent to the circle? Explain..​

Answer 1

AB is not tangent to the circle.

Explanation:

A tangent is a straight line that touches a circle at only one point.

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

Therefore, if AB is tangent to the circle, it will form a right angle with the radius, CA.

To determine if AB is tangent, we can use Pythagoras Theorem.

`\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}`

If AB is tangent, then angle CAB will be a right angle. So AC and AB would be the legs of the right triangle, and BC would be the hypotenuse.

Therefore:

`AC^2+AB^2=BC^2`

Substitute the values into the equation:

`7^2+12^2=15^2`

`49+144=225`

`193 = 225 \; \leftarrow\; \sf not\;true`

As 193 ≠ 225, the equation does not hold, hence proving that AB is not tangent to the circle.