If is circumscribed about the circle in such a way that m = 90 ° and m = 110 ° , which is true?
A) cannot be a right angle
B)m m
C)m = 200 °

Question

If  is circumscribed about the circle in such a way that m  = 90 ° and m  = 110 ° , which is true?
A) cannot be a right angle 
B)m m 
C)m = 200 °

Quizplus · Accepted Answer

If m 11ebfb55_24af_e061_9d86_7fa1d6a7d4f5_TBX8811_11 = 90 °, then 11ebfb55_24af_e064_9d86_a57dda86f0cb_TBX8811_11 cannot be a right angle (choice A is false). If m 11ebfb55_24af_e062_9d86_c335ea9db2e1_TBX8811_11 = 90°, then it is perpendicular to the circle and must intersect the diameter passing through the center of the circle. Since m 11ebfb55_24af_e063_9d86_950078b5b5af_TBX8811_11 = 110°, the other endpoint of the diameter lies on the minor arc between 11ebfb55_24af_e062_9d86_c335ea9db2e1_TBX8811_11 and 11ebfb55_24af_e064_9d86_a57dda86f0cb_TBX8811_11, which means that TBX8811_11 must lie outside of the circle. Since TBX8811_11 lies outside the circle, m 11ebfb55_24b0_0778_9d86_b142b388320a_TBX8811_11 is the measure of the minor arc that TBX8811_11 cuts off, and it is equal to twice the measure of the inscribed angle 11ebfb55_24af_e062_9d86_c335ea9db2e1_TBX8811_11 (which is 90°). Thus, m 11ebfb55_24b0_0778_9d86_b142b388320a_TBX8811_11 = 180°, so choice C is false. Since TBX8811_11 lies outside the circle, choice D, which implies that TBX8811_11 lies inside the circle, is false. Therefore, the only true statement is choice B, which states that m 11ebfb55_24af_e065_9d86_f7a884990877_TBX8811_11 is equal to m 11ebfb55_24af_e067_9d86_cb494296d8bc_TBX8811_11, as they are opposite angles in a cyclic quadrilateral.

If Is Circumscribed About the Circle in Such a Way