Question

Which figure shows a line tangent to the circle?

A circle is shown. A line with length 3 is drawn from the middle point to a point on the circle. A line with length 6 is drawn from that point to a point outside of the circle. Another line with length 9 is drawn from that point to the middle point to form a triangle.

A circle is shown. A line with length 5 is drawn from the middle point to a point on the circle. A line with length 5 is drawn from that point to a point outside of the circle. Another line with length 10 is drawn from that point to the middle point to form a triangle.

A circle is shown. A line with length 3 is drawn from the middle point to a point on the circle. A line with length 4 is drawn from that point to a point outside of the circle. Another line with length 5 is drawn from that point to the middle point to form a triangle.

Answer 1

The third figure.

Reason: A tangent at a point is perpendicular to the radius to that point. In the third figure OA = 3, AP = 4, OP = 5, and 3^2 + 4^2 = 5^2, so triangle OAP is right-angled at A (OA ⟂ AP) — AP is tangent.

In the first two figures OP = OA + AP (9 = 3+6 and 10 = 5+5), so O, A, P are collinear and the line through A is not tangent.