Geometry Problems with Solutions and Answers for Grade 12

Grade 12
geometry problems with detailed solutions are presented. These geometry problems are presented here to help you think and learn how to solve problems. Do not give up quickly if a problem is a challenging one. Spend time solving these problems and work in groups if possible as group work encourages you to discuss ideas and learn from each other. We learn by solving problems that we do not know how solve at first.

In the triangle ABC sides AB and CB have equal lengths and the measure of angle ABC is equal to 36 degrees. What is the measure of angle BOC where O is the center of the circle?

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Circles C1 and C2 have equal radii and are tangent to that same line L. Circle C3 is tangent to C1 and C2. x is the distance between the between the centers of C1 and C2. Find the distance h, from the center of C3 to line L, in terms of x and the radii of the three circles.

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All three circles are tangent to the same line and to each other. Circles C2 and C3 have equal radii. Find the radius of C2 if the radius of C1 is equal to 10 cm.

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CD is parallel to AB and the measure of angle t is equal to 90 degrees. Find the area of the circle in terms of x.

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The shaded region below is the common area to four semicircles whose diameters are the sides of the square with side length 4x. Find the area of the shaded region in terms of x.

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The two circles below are concentric (have same center). The length of the chord tangent to the smaller circle is equal to 20 mm. What is the area of the ring (shaded area) between the two circles?

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Find a, b and c so that the quadrilateral is a parallelogram with area equal to 80 square units.

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A right triangle is shown below. Find the lengths x, y and z.

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A rectangle is shown below. Find the length x.

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The two circles below have equal radii of 4 units each and the distance between their centers is 6 units. Find the area of the shaded region.