Geometry Answers

Find the length of the arc on the unit circle with the given central angles

a. 315º

b. 240º

The circumferences of two circles are 3 m. and 9πm. What is the ratio of the areas of the circle?

Using the formula for the length of the arc, compute s, r or θ which ever is missing.

a. s = 6π r = 8

b. s = 10π r = 8

Formulate at least two problems invovlimg arcs and central angles,thensolve

ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a

and AQ = b, find in terms of a and b, the directed line segments (i) AB

Pyramid A is a square pyramid with a base side length of 12 inches and a height of 8 inches. Pyramid B has a volume of 20,736 in3. How many times bigger is the volume of pyramid B than pyramid A? (5 points)

3. OABC is a tetrahedron and OA = a, OB = b and OC = c. The points P and Q

are such that OA = AP and 2OB = BQ. The point M is the midpoint of P Q. Find

(i) AB, (ii) PQ, (iii) CQ, (iv) QM, (v) MB and (vi) OM in terms of a, b and c.

4. ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x

and AC = 2y, express the vectors (i) BC, (ii) PQ, (iii) PC, (iv) BQ in terms of x

and y. What can you deduce about the directed line-segments BC and PQ?

5. ABC is a triangle. If D is the midpoint of AC, show that BA + BC = 2BD.

6. ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal

and parallel to BC.

7. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a

and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD,

(iii) BD, (iv) AC.

8. ABC is a triangle and P is any point in BC. If PQ is the resultant of AP, PB, PC,

show that ABQC is a parallelogram, and Q is therefore a fixed point.

ABC is a triangle and P is any point in BC. If PQ is the resultant of AP, PB, PC, show that ABQC is a parallelogram, and Q is therefore a fixed point

ABCD is a square and P, Q are the mid points of BC, CD respectively. If AP = a and AQ = b, find in terms of a and b, the directed line segments 

I. AB

II. AD

III. BD 

IV. AC