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A single lane street 12ft wide goes through a semicircular tunnel with radius 10ft. How high is the tunnel at the edge of each lane?


A diameter ofthe circle is ....... radius



paperweight in the shape of the pyramid has a regular hexagonal base with a perimeter that measures 16.8cm. The pyramid has a height of 4.7 cm and the distance from the center of the base to the midpoint of each side 2.,9 cm. What is the surface area of the paperweight?
. Prove the corollary of the tangent theorem: If A and B are points on
circle O and line segments PA and PB are tangent to the circle, show that line segment PA is congruent to line segment PB
and line segment PO bisects angle APB

Prove that the line joining the midpoints of the base and summit of a Saccheri Quadrilateral is the perpendicular bisector of both the base and the summit


You have given an equal-sided triangle with side length a. A straight line connects the center of the bottom side to the border of the triangle with an angle of α. Derive an expression for the enclosed area A(α) with respect to the angle
prove that two chords of a circle are congruent if and only if they subtend arcs of equal measure.

prove that the line joining the midpoints of the base and summit of a saccheri quadrilateral is the perpendicular bisector of both the base and the summit .


 Amy measures the slant height of a cone-shaped cup and finds that it is 12 cm. The height is 10 cm. Determine the volume of water in the cup if Amy fills it to the top.


Angle bisectors of angles BAC and BCA of triangle ABC intersect its altitude BH at points P and
Q respectively. It is known that point H lies on side AC, P is situated between H and Q,
BQ = 54,5, QP = 17,5, PH = 36. Find the area S of triangle ABC. As the answer,
indicate the value of S√3 .
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