An angle whose _______________ is ______ the circle and whose sides contain chords of the circle. An angle whose _________________ is the _________________ of the circle and whose sides are radii of the circle. Measure of an inscribed Angle Measure of a central Angle m ∠ ADB = ½ m AB m∠APB = m AB A P D B B A Ex.: B A 1. If mBC = 80, then C 2. If mBAC = _____°. mBAC = 35°, then m BC = _____°. Theorem 10.8: If two inscribed angles of a circle intercept the same arc, then __________________ _________________________________________ intercepted arc Angle A = Angle B If all the vertices of a polygon lie on a circle, the polygon is __________________ in the circle and the circle is _________________ about the polygon. 10.4 Notes: 1 B Theorem 10.9: If a right triangle is inscribed in a circle, then _____________________________________ Converse is also true A C _____________________________________ AC is a diameter, then m∠B = 90o Theorem 10.10: A quadrilateral can be inscribed in a circle iff its ____________________________________________ m∠D + m∠F = m∠E + m∠G = 180o Ex.: 1. Draw a circle with inscribed quadrilateral ABCD. 2. If mA = 50, then mC = _____. 3. If mB = (2x + 5)° and mD = (3x – 10)°, find x and mB. Show algebra. 4. CHALLENGE! If mB = (x2 + 20)° and mD = (9x – 2)°, find x and mB. Show algebra. 10.4 Notes: 2 Find the indicated measure(s). 1.) m∠A =_______ 2.) m∠A=_______ 3.) m∠A=_______ m∠C=_______ 4.) m∠C =_______ 5.) m BC =_______ 7. ) Find the indicated measure in 6.) m∠C =_______ M. a.) m∠PNO =_______ b.) m∠QNP =_______ c.) m PQ =_______ d.) m QO =_______ e.) m∠NMO =_______ f.) m NOP =_______ g.) m∠QMP =_______ h.) m OQN =_______ 8.) Find the value of each variable. Explain. A 9.) Find the values of x and y. Then find the measures of the interior angles of the polygon. A B (17y)° y° x° D 100° 102° C (5x)° (7x)° B (19y)° C D x = ______ y = ______ x = _______ y = ______ z = mBCD = ________ m∠DAB = _______ m∠ABC = _______ m∠BCD = _______ m∠CDA = ________ 10.4 Notes: 3