Math 9 – Circle Geometry Take-Home Test Name: __________________________________ Date: ____________________________________ Part 1: Matching (1/2 mark each) / Part 2: Written Response (1 mark each) ____ 1) Tangents from an external point are equal ____ 2) A tangent is perpendicular to the radius at the point of contact a) b) c) d) e) f) g) h) 3) The line joining the midpoint of the chord to the centre is perpendicular to the chord. ____ 4) Central angles containing equal chords or arcs are equal. ____ 5) Inscribed angles containing the same or equal chords or arcs are equal. ____ ____ 6) The perpendicular bisector of a chord passes through the centre of the circle. ____ 7) The line through the centre, perpendicular to a chord, bisects the chord. ____ 8) Opposite angles of a cyclic quadrilateral are supplementary. ____ 9) An inscribed angle in a semicircle measures . j) i) 10) An inscribed angle equals half the central angle containing the same chord or arc, or an equal chord or arc. ____ - Answer each of the following. Remember to put in your degree symbols. 1) 2) x= x= 3) 4) m1 m2 VUT x= QXR y= 5) 6) x= x= y= 7) 8) and are tangent lines x= PY 9) 10) is tangent to the circle at the point a TOS RSU 11) 12) 1 a 2 b 3 4 c 5 d 13) 14) AEF 1 BFE 2 DGE 3 15) 16) 1 BDC 2 DCB 3 17) DBC 18) XY 4 XA 5 6 AB 7 19) 20) 3 4 4 5 21) 22) 6 ABC 7 4 8 5 23) 24) 4 FEH 5 GEF EHG ABC Part 3: Application Problems (5 marks each): - Work must be shown for full marks 1) A 20 cm cut is made 9 cm from the outside edge of a circle. What is the radius of the circle (accurate to the nearest tenth.) 2) In the circle, and are parallel chords apart. If , then how far is from the centre of the circle? and