Given that ut is the perpendicular bisector of ab, where t is on ab, find the length of at given at = 3x + 6 and tb = 42 - x.

make at equal to tb. solve for x, then plug the answer you got for x into the equation 3x plus 6, and the answer you get is the length of at

A perpendicular bisector cuts the segment into two equal pieces. We're told that T bisects AB, and UT is the perpendicular bisector.

So, AT = TB.

We're told that AT = 3x + 6 and TB = 42 - x. We set them equal to each other, find x, and report the length.

3x + 6 = 42 - x

4x + 6 = 42

4x = 36

x = 9

So AT's length is 3 * 9 + 6 = 27 + 6 = 33. TB's length is 33 too.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq