Consolidate understanding of tangent properties and apply them to mixed-difficulty proofs and calculations.
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Complex figures from exercises are best provided directly to the student.
Clean scientific diagram of a circle with center O, circumscribed by a quadrilateral ABCD. The quadrilateral touches the…
Summary of learning outcomes.
Progressive difficulty MCQs spanning the chapter.
If TP and TQ are two tangents to a circle with centre O so that , then is equal to:
Prove AB + CD = AD + BC for a circumscribed quadrilateral.
Use the property of tangent lengths to prove: for a circumscribed quadrilateral .
Identify the theorem about tangents from an external point.
Break down each side of the quadrilateral into two tangent segments and sum the equations.
Think about fitting shapes into constrained spaces.
Prove angle AOB = 90 degrees.
Given two parallel tangents and to a circle with center , and a third tangent with point of contact intersecting at and at . Prove that .
Look at the triangles formed by the center, the external points A and B, and the points of contact.
Use the straight line passing through the center to sum the angles to 180 degrees, then solve for angle AOB.
Prove that a parallelogram circumscribing a circle is a rhombus.
Use the property of a circumscribed quadrilateral and the properties of a parallelogram to show that all four sides are equal.
Recall the sum of opposite sides for any circumscribed quadrilateral.
Combine the tangent sum property with the fact that opposite sides of a parallelogram are equal.