Question

If line PB is tangent to Circle A and


Find ABP :_____

Find APB :_____

Answer 1

Angle APB would be 90° since line PB is tangent to Circle A at point B, implying PA (radius) is perpendicular to PB (tangent). Without further details, angle ABP cannot be precisely determined.

Step-by-step explanation:

To determine the angles ABP and APB when line PB is tangent to Circle A, we need to establish a relationship between the angles using the properties of a tangent and a radius. By definition, a tangent is perpendicular to the radius at the point of tangency. Assuming that PA is the radius and PB is the tangent, angle APB would be a right angle (90°).

If AB is a chord and PB a tangent, then angle ABP would be defined by the angle created between the chord and the tangent. Without additional information about the lengths of segments or other angles, we cannot numerically determine angle ABP. However, by the triangle sum theorem, we know that the sum of angles within a triangle is 180°. Since PA is the radius and forms a right angle at B, and assuming we denote angle PAB as \( \theta \), we can say:

• Angle APB = 90° (since PA \(\perp\) PB)
• Angle ABP + Angle APB + Angle PAB = 180°
• Angle ABP = 180° - 90° - \(\theta\)

Without the measure of angle PAB (\( \theta \)), we can't provide a precise measurement for angle ABP.

Answer 2

The tangent of a circle is perpendicular to the radius at the point of tangency, so
`m\angle ABP=\boxed{90^(\circ)}`.

There is insufficient information to find
`m\angle APB`.