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Geometry

Tangent and Secant Lines

Concept Quizzes

Tangent and Secant Lines Warmup
Circles - Intersecting Chords
Tangent - Perpendicular to Radius
Alternate Segment Theorem
Tangent - Subtended Arc
Two Secants
Tangent-Secant
Tangent to Circles - Problem Solving

Challenge Quizzes

Tangent and Secant Lines: Level 2 Challenges
Tangent and Secant Lines: Level 3 Challenges

Tangent - Perpendicular to Radius

What is the area of the shaded quadrilateral shown above?

89 87 83 85

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by Brilliant Staff

Two circles $M$ and $N$ are tangent to two perpendicular lines that intersect at point $L,$ as shown in the above diagram. If the radii of the two circles are $r_{1}=16$ and $r_{2}=8,$ respectively, what is the distance between $M$ and $N?$

Note: The above diagram is not drawn to scale.

{28}\sqrt{3}

{26}\sqrt{2}

{22}\sqrt{3}

{24}\sqrt{2}

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by Brilliant Staff

In the above diagram, a sphere is inscribed in a right circular cone. If the radius of the sphere is $24$ and the radius of the base circle of the cone is $48,$ what is the height of the cone?

Note: the above diagram is not drawn to the scale

60 68 66 64

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by Brilliant Staff

$\overline{AN}$ and $\overline{AB}$ are both tangent to circle $O.$ If the radius of the circle is $44$ and $\angle NAB={30}^\circ,$ what is the distance between $N$ and $\overline {AB}?$

{44}\sqrt{2}+{22}

{44}\sqrt{3}+{44}

{22}\sqrt{2}+{44}

{22}\sqrt{3}+{44}

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by Brilliant Staff

In the above diagram, $\triangle ABC$ and $\triangle DEF$ are both equilateral triangles. If the circle in the diagram with center $O$ is the circumscribed circle of $\triangle DEF$ and the inscribed circle in $\triangle ABC,$ what is the ratio $\lvert\overline {AB}\rvert : \lvert\overline {DE}\rvert?$

Note: $\lvert\overline {AB}\rvert$ denotes the length of $\overline {AB}.$

\sqrt{2} : {1}

{2} : {1}

\sqrt{3} : {1}

{3} : {1}

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by Brilliant Staff