Circle theorem 5 and 6 07 01 14

Circle theorem 5 and 6 07. 01. 14

Introduction

Theorem 5 The Alternate Segment Theorem. The angle between a tangent and a chord through the point of contact is equal to the angle subtended by that chord in the alternate segment. Find the missing angles below giving reasons in each case. xo yo yo xo o 60 xo o y angle x = 45 o (Alt Seg) angle y = 60 o (Alt Seg) angle z = 75 o angle sum triangle zo 45 o Th 5

Find angle ATS and angle TSR B TSR = 70 T 70 80 A 70 S R

Find angle ATS and angle TSR B TSR = 70 T 70 80 80 A 70 S R ATS = 80

Theorem 6 Cyclic Quadrilateral Theorem. The opposite angles of a cyclic quadrilateral are supplementary. (They sum to 180 o) y Th 6 x w p q z s r Angles x + z = 180 o Angles p + r = 180 o Angles y + w = 180 o Angles q + s = 180 o

Theorem 6 Cyclic Quadrilateral Theorem. The opposite angles of a cyclic quadrilateral are supplementary. (They sum to 180 o) 70 o x y 110 o Find the missing angles below given reasons in each case. r q p 85 o 135 o angle x = 180 – 85 = 95 o (cyclic quad) angle p = angle y = 180 – 110 = 70 o (cyclic quad) angle q = 180 – 70 = 110 o (cyclic quad) angle r = 180 – 45 = 135 o (cyclic quad) 180 – 135 = 45 o (straight line)

Angles in a cyclic quadrilateral

Start the clip at 2. 32 mins