Question

point o is the center of the circle.
what is the perimeter of quadrilateral dobc?
14 units
16 units
22 units
28 units

Explanation:

Step1: Identify radii and tangents

OD and OB are radii of the circle, so \( OD = OB = 6 \). CD and CB are tangents from point C to the circle, so \( CD = CB = 8 \) (tangents from a common external point to a circle are equal).

Step2: Calculate perimeter of DOBC

Perimeter of quadrilateral \( DOBC = OD + OB + BC + CD \). Substitute the values: \( 6 + 6 + 8 + 8 \).

Step3: Compute the sum

\( 6 + 6 + 8 + 8 = 12 + 16 = 28 \)? Wait, no, wait. Wait, maybe I misread. Wait, no, let's check again. Wait, OD is 6, OB is 6, BC is 8, CD is 8? Wait, no, maybe the figure: OD is perpendicular to CD, OB is perpendicular to BC, so triangles ODC and OBC are right triangles. But since CD and CB are tangents, CD = CB. OD and OB are radii, so OD = OB. So perimeter is OD + DB? No, quadrilateral DOBC has sides DO, OB, BC, CD. So DO = 6, OB = 6, BC = 8, CD = 8. So 6 + 6 + 8 + 8 = 28? But the options have 28 as an option. Wait, but let me check again. Wait, maybe the length of OC? No, perimeter is sum of all sides. So DO (6) + OB (6) + BC (8) + CD (8) = 6+6+8+8=28.

Answer:

28 units