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Plane Geometry

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Problem 1: Area of Smaller Segment

A circle is divided into two parts by a chord, 3 cm away from the center. Find the area of the smaller part, in cm square, if the circle has an area of 201 cm square.

Plane Geometry – Problem 1: Area of Smaller Segment – Diagram Plane Geometry – Problem 1: Area of Smaller Segment – Diagram Plane Geometry – Problem 1: Area of Smaller Segment – Diagram

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Plane Geometry – Problem 1: Area of Smaller Segment – Diagram Plane Geometry – Problem 1: Area of Smaller Segment – Diagram Plane Geometry – Problem 1: Area of Smaller Segment – Diagram Plane Geometry – Problem 1: Area of Smaller Segment – Diagram

Problem 2: Area of a Sector given the Perimeter

Determine the area of a sector of a circle if its perimeter is 19 inches and the radius is 6 inches.

Plane Geometry – Problem 2: Area of a Sector given the Perimeter – Diagram Plane Geometry – Problem 2: Area of a Sector given the Perimeter – Diagram Plane Geometry – Problem 2: Area of a Sector given the Perimeter – Diagram

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Plane Geometry – Problem 2: Area of a Sector given the Perimeter – Diagram Plane Geometry – Problem 2: Area of a Sector given the Perimeter – Diagram Plane Geometry – Problem 2: Area of a Sector given the Perimeter – Diagram Plane Geometry – Problem 2: Area of a Sector given the Perimeter – Diagram

Problem 3: Central Angle is Twice the Inscribed Angle

A triangle with an area of 90 cm2 is inscribed in a 20-cm diameter semi-circle such that its vertices touch the semi-circle. If one side of the triangle measures 20 cm, find the other two sides of the triangle.

Plane Geometry – Problem 3: Central Angle is Twice the Inscribed Angle – Diagram Plane Geometry – Problem 3: Central Angle is Twice the Inscribed Angle – Diagram Plane Geometry – Problem 3: Central Angle is Twice the Inscribed Angle – Diagram

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Plane Geometry – Problem 3: Central Angle is Twice the Inscribed Angle – Diagram Plane Geometry – Problem 3: Central Angle is Twice the Inscribed Angle – Diagram Plane Geometry – Problem 3: Central Angle is Twice the Inscribed Angle – Diagram Plane Geometry – Problem 3: Central Angle is Twice the Inscribed Angle – Diagram

Problem 4: Intersecting Chords

Chord AB and CD intersect at point "O". "AO = 8 cm", "CO = 12 cm", and "DO = 20 cm". If "AB" is the diameter of the circle. Calculate the area "OCA".

Plane Geometry – Problem 4: Intersecting Chords – Diagram Plane Geometry – Problem 4: Intersecting Chords – Diagram Plane Geometry – Problem 4: Intersecting Chords – Diagram

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Plane Geometry – Problem 4: Intersecting Chords – Diagram Plane Geometry – Problem 4: Intersecting Chords – Diagram Plane Geometry – Problem 4: Intersecting Chords – Diagram Plane Geometry – Problem 4: Intersecting Chords – Diagram

Problem 5: Rectangular Garden (Worded Problem)

The length of a rectangular garden is 9m longer than its width. If the area of the garden is 78.6 square meters, finds its dimensions.

Plane Geometry – Problem 5: Rectangular Garden (Worded Problem) – Diagram Plane Geometry – Problem 5: Rectangular Garden (Worded Problem) – Diagram Plane Geometry – Problem 5: Rectangular Garden (Worded Problem) – Diagram

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Plane Geometry – Problem 5: Rectangular Garden (Worded Problem) – Diagram Plane Geometry – Problem 5: Rectangular Garden (Worded Problem) – Diagram Plane Geometry – Problem 5: Rectangular Garden (Worded Problem) – Diagram Plane Geometry – Problem 5: Rectangular Garden (Worded Problem) – Diagram

Problem 6: Cyclic Quadrilateral

The sides of a cyclic quadrilateral measures 8cm, 9cm, 12cm, and 7cm, respectively.
a. Find the area of the cyclic quadrilateral.
b. Find the area of the circumscribing circle.

Plane Geometry – Problem 6: Cyclic Quadrilateral – Diagram

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Plane Geometry – Problem 6: Cyclic Quadrilateral – Diagram

Problem 7: General Quadrilateral Building Site

A building site is in the form of a quadrilateral with following sides and angles given. AB = 52.4 m, BC = 28.5 m, CD = 34.6 m, angle B = 72°, and angle D = 75°. Determine the area of the site.

Plane Geometry – Problem 7: General Quadrilateral Building Site – Diagram Plane Geometry – Problem 7: General Quadrilateral Building Site – Diagram Plane Geometry – Problem 7: General Quadrilateral Building Site – Diagram

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Plane Geometry – Problem 7: General Quadrilateral Building Site – Diagram Plane Geometry – Problem 7: General Quadrilateral Building Site – Diagram Plane Geometry – Problem 7: General Quadrilateral Building Site – Diagram Plane Geometry – Problem 7: General Quadrilateral Building Site – Diagram

Problem 8: Hexagon (Polygon General Formulas)

A regular hexagon whose sides measure 30 units each is inscribed in a circle. Determine the following:
a. The number of diagonals
b. The interior angle on each side
c. The radius of the circumscribing circle
d. The length of the apothem
e. The area of the polygon

Plane Geometry – Problem 8: Hexagon (Polygon General Formulas) – Diagram Plane Geometry – Problem 8: Hexagon (Polygon General Formulas) – Diagram Plane Geometry – Problem 8: Hexagon (Polygon General Formulas) – Diagram

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Plane Geometry – Problem 8: Hexagon (Polygon General Formulas) – Diagram Plane Geometry – Problem 8: Hexagon (Polygon General Formulas) – Diagram Plane Geometry – Problem 8: Hexagon (Polygon General Formulas) – Diagram Plane Geometry – Problem 8: Hexagon (Polygon General Formulas) – Diagram

Problem 9: Cyclic Quadrilateral

A cyclic quadrilateral "ABCD" is inside a circle with side AD coinciding with the diameter of the circle. AB = 8cm, BC = 10cm, CD = 12cm. Find the area of the circumscribing circle.

Diagram Diagram Diagram

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Solution
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