Chapter 10: Circle Geometry - McGraw-Hill Ryerson

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$Math and Chemistry - McGraw-Hill Ryerson$

Name: _____________________________________________________ Date: ______________ Point C is the centre of the circle. ∠DAB = 55º A D 55° C CC a) What is the measure of ∠DEB? Show how you know. D A 55° C CC ∠DEB is an angle. (inscribed or central) ∠DEB = ∠DAB because they share the same . ∠DAB is °. So, ∠DEB is °. 8 MHR ● Chapter 10: Circle Geometry DRAFT b) What is the measure of ∠DCB? Show how you know. ∠DCB is a angle. ∠DCB = × ∠ = × ° = ° So, ∠DCB is °. E E B B
Name: _____________________________________________________ Date: ______________ Working Example 2: Use Central and Inscribed Angles to Recognize Relationships Point C is the centre of the circle. diameter AB = 10 cm chord BD = 6 cm a) What is the measure of ∠ADB? Justify your answer. Solution ∠ACB is a central angle. A straight angle measures °. Since AB is a straight line, the central angle ∠ACB = °. ∠ACB is twice the measure of the inscribed angle ∠ADB because they share the same arc, AB. ∠ADB = ∠ACB ÷ 2 6 2 = 6 × 6 = ÷ 2 = ° So, ∠ADB is °. b) What is the length of chord AD? Justify your answer. Solution ∠ADB = 90°, so ΔABD is a right triangle. Use the Pythagorean relationship to find the length of chord AD. AD 2 + BD 2 = AB 2 AD 2 + 6 2 = AD 2 + = 100 DRAFT AD 2 + – = 100 – Subtract 36 from both sides. AD 2 = AD = AD = The length of chord AD is cm. 2 An inscribed angle using the endpoints of a diameter is a right angle. D 6 cm C A B 10 cm AD and BD are the legs and AB is the hypotenuse. 10.1 Exploring Angles in a Circle ● MHR 9
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Chapter 10: Circle Geometry - McGraw-Hill Ryerson

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