Question

BC is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth?

Answer 1

Angles B and C are right angles because a radius of a circle drawn to a tangent to the circle at its outer endpoint is perpendicular to the tangent.

Answer 2

From point D, draw a perpendicular DE segment to segment AB. You can do this because in a plane, through a point outside a line, a line perpendicular to that line may be drawn.

Answer 3

Note that Quadrilateral EBCD must be a rectangle because three of its four interior angles are right angles, the sum of the interior angles is 360. That leaves 90 degrees for the fourth angle.

Answer 4

19.2?

Answer 5

Note that ED = 19 and AB splits into two segments of lengths 7 and 3 based on the notion that opposite sides of a rectangle are congruent.

Answer 6

Now look at triangle EAD with right angle at E. Use the Pythagorean Theorem to compute AD.

Answer 7

@linzie693 >>19.2? Yes, that is what I got - and without guessing. :)

Answer 8

no I did math, I was just asking if I was right.

Answer 9

Good to hear. @linzie693