Tougher cyclic quadrilateral, similar triangle and circle theorem applications.
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Q1 · Advanced Geometry · EASY
In a cyclic quadrilateral ABCD, angle A = 75° and angle B = 105°. What is the measure of angle D?
Q2 · Advanced Geometry · MEDIUM
Two triangles ABC and PQR are similar with AB = 6 cm, BC = 8 cm, and PQ = 9 cm. If the area of triangle ABC is 24 sq cm, what is the area of triangle PQR?
Q3 · Advanced Geometry · MEDIUM
A circle is inscribed in triangle ABC with sides AB = 13 cm, BC = 14 cm, and CA = 15 cm. What is the radius of the inscribed circle?
Q4 · Advanced Geometry · HARD
In a circle with center O, two chords AB and CD intersect at point P inside the circle such that AP = 4 cm, PB = 6 cm, and CP = 3 cm. A tangent from external point Q touches the circle at point T, and QT = 12 cm. If QP passes through the center O and QPT are collinear with P between Q and T, what is the length of the radius of the circle?
Q5 · Advanced Geometry · HARD
A regular hexagon is inscribed in a circle of radius 12 cm. Another circle is inscribed inside the hexagon. What is the ratio of the area of the outer circle to the area of the inner circle?