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
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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 A.∠URJ
B. angle, R, U, W∠RUW
C. angle, U, R, Q∠URQ
D. angle, J, L, O∠JLO
E. angle, J, R, Q∠JRQ
F. angle, R, J, L∠RJL

Answer 1

Answers: B, D, E.

Reasons:
- JR is a radius and RQ is a tangent at R, so JR ⟂ RQ → ∠JRQ is a right angle (E).
- JL is a radius and LO is a tangent at L, so JL ⟂ LO → ∠JLO is a right angle (D).
- RW is a diameter, so any angle subtended by RW on the circle is a right angle (Thales). Thus ∠RUW = 90° (B).

The other angles are not necessarily right in the given configuration.