Points \( P(-3,2), Q(9,10) \) and \( R(\alpha, 4) \) lie on a circle \( C \) with \( P R \) as its diameter. The tangents to \( C \) at the points \( Q \) and \( R \) intersect at the point \( S \). If \( S \) lies on the line \( 2 x-k y=1 \), then \( K \) is equal to [JEE (Main)-2023]

Si un ángulo central mide 50 grados, ¿qué medida tiene el arco que este angulo subtende?

1. Bayangan dari titik \( (3,6) \) yang ditranslasikan \( T\binom{-4}{5} \) kemudian dilanjutkan refleksi terhadap sumbu \( x \) adalah \( \ldots \) \( \begin{array}{llll}\text { A. }\binom{7}{11} & \text { B. }\binom{1}{11} & \text { C. }\binom{-1}{-11} & \text { D. }\binom{-1}{11} \\ \text { E. }\binom{-7}{-11}\end{array} \)

Given your sister's incomplete text, "Meet me at the trails located at \( (-2 \), " Explain why the trails must be in quadrant 2 or quadrant 3 .

Teresa needs to cut a triangular piece of tile for a mosaic. In order to cut it properly, she needs to know the measure of the unknown angle? \( { }^{\circ} \) as shown in the figure. The lengths of \( K L, L M \), and \( M K \) are 105 millimeters, 123 millimeters, and 182 millimeters respectively. What is the value of the unknown angle? (Round your answer to the nearest degree if necessary.)

2. Titik \( L(9,-2) \) dicerminkan terhadap \( x=2 \) kemudian dilanjutkan translasi \( T\binom{-2}{4} \), bayangan titik \( L \) adalah \( \ldots \) \( \begin{array}{llll}\text { A. }\binom{-5}{2} & \text { B. }\binom{-3}{4} & \text { C. }\binom{7}{6} & \text { D. }\binom{7}{2}\end{array} \)