Arcs, chords, tangents, inscribed angles Knowledge-Based Download PDF

Questions

1. 1.

   In a circle, diameter $CD$ is perpendicular to chord $AB$, with point $D$ lying on minor arc $AB$. If the measure of arc $AD$ is 52°, what is the measure of the inscribed angle $\angle ABC$?

   • A) 52°
   • B) 64°
   • C) 76°
   • D) 38°
2. 2.

   A line tangent to a circle touches the circle at point $T$, and chord $AB$ is parallel to this tangent line. If the inscribed angle $\angle TAB$ measures $38^\circ$, what is the measure of minor arc $AB$?

   • A) $152^\circ$
   • B) $76^\circ$
   • C) $114^\circ$
   • D) $104^\circ$
3. 3.

   In a circle, chords $AB$ and $AC$ have equal length, and the measure of minor arc $BC$ is $104^\circ$. If line $l$ is tangent to the circle at point $A$, what is the measure of the acute angle between chord $AB$ and line $l$?

   • A) $52^\circ$
   • B) $58^\circ$
   • C) $64^\circ$
   • D) $76^\circ$
4. 4.

   Two chords, AB and CD, intersect at an interior point X of a circle. If the inscribed angle $\angle ADC$ measures 34° and $\angle AXC = 82°$, what is the measure of arc BD?

   • A) 48°
   • B) 68°
   • C) 96°
   • D) 130°