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Line \(BD\) is tangent to a circle with diameter \(AB\). Explain why the measure of angle \(BCA\) must equal the measure of angle \(ABD\).
Line \(AC\) is perpendicular to the circle centered at \(O\) with radius 1 unit. The length of \(AC\) is 1.5 units. Find the length of segment \(AB\).
Technology required. Line \(PD\) is tangent to a circle of radius 1 unit centered at \(O\). The length of \(PD\) is 1.2 units. The length of \(AB\) is 1.7 units. Which point on the circle is closest to point \(P\)?
Circle center O, diameter A D. Line P D is tangent to circle. Points B and C lie on circle. Segment A P drawn, passing through B. Segment O P drawn, passing through C. Segment A B labeled 1 point 7. Segment P D labeled 1 point 2.
point \(A\)
point \(B\)
point \(C\)
point \(D\)
The arc from \(A\) to \(B\) not passing through \(C\) measures 50 degrees. Select all the true statements.
Angle \(BCA\) measures 50 degrees.
Angle \(BCA\) measures 25 degrees.
Angle \(BOA\) measures 50 degrees.
The arc from \(B\) to \(C\) not passing through \(A\) measures 180 degrees.
Angles \(CBO\) and \(CAO\) are congruent.
Chords \(AC\) and \(DB\) intersect at point \(E\). List 3 pairs of angles that must be congruent.
The image shows a circle with diameters \(AC\) and \(BD\). Prove that chords \(BC\) and \(AD\) (not drawn) are congruent.