Question

Draw a circle of radius 2.25 cm

Answer 1

Answer:

Step-by-step explanation:

1 OM = MP = JM M was constructed as the midpoint of OP (See Constructing the perpendicular bisector of a line segment for method and proof) and JM=OM because JM was constructed with compass width set from MO

2 JMO is an isosceles triangle JM=OM from (1)

3 ∠JMO = 180–2(∠OJM) Interior angles of a triangle add to 180°. Base angles of isosceles triangles are equal.

4 JMP is an isosceles triangle JM=MP from (1)

5 ∠JMP = 180–2(∠MJP) Interior angles of a triangle add to 180°. Base angles of isosceles triangles are equal.

6 ∠JMP + ∠JMO = 180 ∠JMP and ∠JMO form a linear pair

7 ∠OJP is a right angle  

Substituting (3) and (5) into (6):

(180–2∠MJP) + (180–2∠OJM) = 180

Remove parentheses and subtract 360 from both sides:

–2∠MJP –2∠OJM = –180

Divide through by –2::

∠MJP + ∠OJM = 90

8 JP is a tangent to circle O and passes through P JP is a tangent to O because it touches the circle at J and is at right angles to a radius at the contact point.

(see Tangent to a circle.)

p KP is a tangent to circle O and passes through P As above but using point K instead of J