Geometry, question 2, grade 9

11/07/2016 Grade 9 2,615


Draw a circle C(O,4cm) of diameter [AB], Plot the midpoint M of [OB] and draw [CD] the perpendicular to [OB] at M.

a) Show that COB is an equilateral triangle, then deduce the nature of triangle MOC.

b) E is the symmetric of C w.r.t B :

i) Show that (ED) is orthogonal to (CD).

ii) Prove that triangle DCM is similar to triangle MCB and write the ratio of similarity.

iii) Deduce that triangle DCM is an enlargement of triangle MCB with a certain scale factor to be determined.

iv) Draw triangle CPK, knowing that triangle CMB is the reduction of triangle CPK by scale factor :1/3