Question

The figure below shows a circle with center JJ, diameter start overline, R, W, end overline
RW
, and tangents R, Q, with, left-right arrow, on top
RQ
​
and L, O, with, left-right arrow, on top
LO
. Which of the angles must be right angles? Select all that apply. angle, U, R, J∠URJ
A. angle, R, U, W∠RUW
B. angle, U, R, Q∠URQ
C. angle, J, L, O∠JLO
D. angle, J, R, Q∠JRQ
E. angle, R, J, L∠RJL

Answer 1

B and D.

- B (∠RUW): RW is a diameter, so any angle subtending that diameter with its vertex on the circle is a right angle (Thales' theorem).
- D (∠JRQ): JR is a radius and RQ is a tangent at R, and a radius to the point of tangency is perpendicular to the tangent, so ∠JRQ = 90°.