23.02 Cyclic quadrilaterals (Extended)
The diagram shows a cyclic quadrilateral. Solve for m.
In the following figure, ABCD is inscribed inside a circle:
What is the sum of any two opposite angles in the quadrilateral ABCD?
Can a parallelogram be inscribed inside a circle? Explain your answer.
Can a rectangle be inscribed inside a circle? Explain your answer.
Consider the following figure:
Determine the value of d.
Find the value of the pronumerals in the following diagrams. Give reasons for your answer.
Find the value of y in the following diagram:
Consider the following figure:
Find the value of x.
Find the value of y.
In the diagram, \angle AOC = 174 \degree, where O is the centre of the circle:
Determine the size of reflex \angle AOC.
Determine the size of \angle ABC.
Can a circle be drawn through the vertices of quadrilateral OABC? Explain your answer.
In the diagram, O is the centre of the circle:
Solve for the value of m, giving reasons for your answer.
Solve for the value of n, giving reasons for your answer.
In the diagram, O is the centre of the circle.
Solve for p, giving reasons for your answer.
Solve for q, giving reasons for your answer.
Solve for r, giving reasons for your answer.
Consider the given diagram:
Find the value of p, giving reasons for your answer.
Find the value of q, giving reasons for your answer.
In the diagram, \angle ADB = 32 \degree and \angle DBA = 43 \degree. Find the size of the angle marked m, giving reasons for your answer.
In the diagram, AB \parallel DC and \\ \angle BCE = 98 \degree . DC is produced to point E.
Find the size of \angle BAD.
In the diagram, \angle DBA = 27, \angle CAB = 49, \angle CBD = 21 and \angle ABD = m. Solve for m, giving reasons.
In the following figure, consider the two circles intersect at points B and E.
If \angle BCD=94\degree. Find \angle BAF.
In the diagram, O is the centre of the circle. Show that x and y are supplementary angles.
In the diagram, ABCD is an isosceles trapezium, so AD = BC.
Prove that the points A, B, C and D are concyclic.
Consider the following diagram:
Prove that \angle BAC=126-z.
Consider the following diagram:
Prove AD || CF.
Consider the following diagram:
Prove that x = y.
Consider the figure:
Prove that \angle ABC=\angle CDE .
By proving two similar triangles, Prove that \angle BAD and \angle DCE are equal.
Hence prove that \\ EB \times EC = ED \times EA.
