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

Explanation:

Step1: Determine the lengths of the sides

Since (OD) and (OB) are radii of the circle. Let (OD = OB=r). In right - triangle (ODC), (OD = 6) (given), so (OB = 6). In right - triangle (OBC), (OB = 6) and (BC = 8). In right - triangle (ODC), (OD = 6) and (DC) can be found using the Pythagorean theorem. In right - triangle (OBC), (OB = 6) and (BC = 8), then by the Pythagorean theorem (OC=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10). Also, in right - triangle (ODC), (OD = 6), assume (OC) is the hypotenuse, and since (OC = 10), (DC = 8) (using (a^{2}+b^{2}=c^{2}), (c = 10), (a = 6), then (b=\sqrt{c^{2}-a^{2}}=\sqrt{100 - 36}=\sqrt{64}=8)).

Step2: Calculate the perimeter of (DOBC)

The perimeter (P) of quadrilateral (DOBC) is (P=OD + OB+BC + DC). Substitute (OD = 6), (OB = 6), (BC = 8), (DC = 8) into the formula. (P=6 + 6+8 + 8=28).

Answer:

28 units