Special Segments — Unit test Answers

Circle D is inscribed with triangle A B C. The measure of arc A B is 76 degrees. Point E is on the circle between points B and C.

Circle D is shown. Angle A C B intercepts arc A B. Arc A B has a measure of 76 degrees.

A circle is shown. Secants D E and A E intersect at point E outside of the circle. Secant D E intersects the circle at point C and secant A E intersects the circle at point B. The length of D C is 1, the length of C E is x + 4, the length of A B is 11, and the length of B E is x + 1.

AD and MN are chords that intersect at point B.

Circle T is shown. Angle Q S R intercepts arc Q R. Angle Q S R is 52 degrees.

Line segments XY and ZY are tangent to circle O.

A circle is shown. Secant A D and tangent E D intersect at point D outside of the circle. Secant A D intersects the circle at point B. The length of A B is a, the length of B D is 10, and the length of D E is 12.

Line segment SU is a diameter of circle V.

Line EF is tangent to circle G at point A.

Given: quadrilateral ABCD inscribed in a circleProve: ∠A and ∠C are supplementary, ∠B and ∠D are supplementaryLet the measure of = a°. Because and form a circle, and a circle measures 360°, the measure of is 360 – a°. Because of the ________ theorem, m∠A = degrees and m∠C = degrees. The sum of the measures of angles A and C is degrees, which is equal to , or 180°. Therefore, angles A and C are supplementary because their measures add up to 180°. Angles B and D are supplementary because the sum of the measures of the angles in a quadrilateral is 360°. m∠A + m∠C + m∠B + m∠D = 360°, and using substitution, 180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°.What is the missing information in the paragraph proof?

Line segment GJ is a diameter of circle L. Angle K measures (4x + 6)°.

A circle is shown. Secants S V and T V intersect at point V outside of the circle. Secant S V intersects the circle at point W. Secant T V intersects the circle at point U. The length of T U is y minus 2, the length of U V is 8, the length of S W is y +4, and the length of W V is 6.

Line segment BA is tangent to the circle.

Circle C is inscribed in triangle QSU.

AX and EX are secant segments that intersect at point X.

Angle BAC measures 56°.

Circle G is inscribed with triangle E F D. Point C is on the circle between points E and F. Angle E is 79 degrees. The measure of arc E D is 104 degrees.

In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°.

Given: Circle M with inscribed and congruent radii JM and MLProve: m =

Angle ABD measures (4x + 10)o. Angle ACD measures (5x − 2)o.