Advanced Geometry
Tougher cyclic quadrilateral, similar triangle and circle theorem applications.
Test yourself on Advanced Geometry
5 real SZF IOM questions with instant answers — no signup, ~3 minutes.
Study notes are still being prepared.
Don't wait — Shishya can teach you this topic right now, on demand.
Ask Shishya to teach this →Need more? Ask Shishya
Shishya is your personal tutor for this topic. Pick a starter or open a free chat.
- Go deeper on this topicGo deeper on Advanced Geometry for SZF IOM — examples and edge cases I should know.
- Show me exam shortcutsGive me 3 fastest shortcuts to solve Advanced Geometry questions in the exam.
- What mistakes should I avoid?What are the most common mistakes students make on Advanced Geometry? How do I avoid them?
- Quiz me adaptivelyQuiz me on Advanced Geometry — start with one easy question, then go harder based on how I answer.
Practice this topic
Take a full mock →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?