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B. Line Perpendicular to a Plane4.A nd B are two points in the space. Distances between A, B and a plane P are 8 cm and 4 cm, respectively. The distance between their intersection points with the plane P is 9 cm. Find the distance between A and B if; a) A and B are in the same side of the plane. b)A and B are in opposite sides of the plane.
A is a point on circle such that PA ⊥ α where P is not in α. If PT ⊥ m, PT = 10 cm, and PA = 8 cm, find the radius of the circle.
Find AC.
7.There is a circle in a plane. AB is the diameter of the circle. From point A we draw perpendicular line PA, to the plane. Given that PA = 5 cm and the radius of the cirle is 6 cm. Find the distance between the point P and the farrest point of the circle.
the plane of equilateral triangle ABC at its centroid G. If m(∠AFP) = 45°, what is
9.In the figure DDBC is an isosceles right triangle in the plane E. AD is perpendicular to plane E. Given that BD = 6 cm and DABC is an equilateral triangle. Find AD.
If m(∠APB) = m(∠APC) = 45° and m(∠BPC) = 60°, find m(∠BAC). 11.Show that if two planes are perpendicular to the same line then these planes are parallel.
13.State the following as true or false. a.If a line is perpendicular to any line in a plane then it is perpendicular to the plane. b.From any point of a line we can draw only one perpendicular to this line in space and in plane. c. In plane P there are two lines d and l. All lines which are perpendicular to both of d and l are perpendicular to plane P.
15.A triangle DABC is given in space. What is the set of all points which are equidistant from the vertices of the triangle.
m(<PAH) = 45°, m(<PBH) = 50°, m(<PCH) = 60°. State the following as true or false. a. PA > PB b. PA < PC c. PH = AH d. PH > CH e. PB < PC f. AH > BH g. HB > HC
17.In the figure PH is perpendicular to plane E. Given that PA > PB > PC. How do we order AH, BH and CH?
19.In a plane there are two parallel lines d and k. A and B are two points on line d and AB = 6 cm. If the distance between these two lines is 5 cm find the area of DABC where C is a point on line k.
20.In the figure PT is perpendicular to plane E. ATB is a right triangle with AB = 17 cm. If PA = 25 cm and PT = 24 cm find BT.
KD KD = 5 cm. Find the area of DACK.
22.In the figure the line CD is perpendicular to plane M at point O. Given that OA = BO. Prove that DABC is isosceles triangle.
AB = 13 cm, BK = 12 cm, KD = 24 cm and PD = 7 cm. Find A(DACP). 24.Two airplains with the same velocity are flying from the same plane at the same time. They make a 60° and 45° angles with the plane, respectively. When they collide they have 9000 m height. What was the distance between them initially?
AP = 16 cm, BQ = 8 cm and PQ = 18 cm. What is the minimum value of AC + BC. Date: 2015-12-11; view: 1846
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