Question

13. Given that OA = 12, OB = 6.and mZBAC = 60°,find the followinga) OC=b) ED =c) AB =сd) AC =e) m BAO =E00Bf) mZOCAEg) m AOC =Dh) mZEOC =i) EA =

Answer 1

Part a

Find out OC

In this problem

OC=OB=6 -----> because triangles AOB and AOC are congruent

Part b

Find out ED

ED is a diameter

so

ED=2*OC ----> diameter is two times the radius

ED=2*6=12 units

Part c

Find out AB

In the right triangle AOB

Applying Pythagorean Theorem

OA^2=OB^2+AB^2

12^=6^2+AB^2

AB^2=144-36

AB^2=108

AB=√108

Part d

Find out AC

we have that

AC=AB -----> because triangles AOB and AOC are congruent

so

AC=√108

Part e

Find out mwe have that

m given

OA is the angle bisector of mthat means

mm

Part f

Find out mm because OC is perpendicular to AC

Part g

Find out mwe have that

m by complementary angles in a right triangle

mmm

Part h

Find out mwe have that

mso

m