Plane Geometry With Problems And Applications
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3. Is the construction possible when all three lines are parallel? Why?
STRAIGHT LINES AND CIRCLES. 105 4. If two sides of the triangle are produced, as AB and AD in the figure of § 227, construct a circle tangent to the side BD and to the prolongations of the sides AB and AD.
This is called an escribed circle of the triangle.
5. How many circles can be constructed tangent to each of three straight lines if they are not concurrent and no two of them are parallel?
6. Draw a triangle and construc...t its inscribed and circumscribed circles and its three escribed circles.
230. Pkoblem. From a given point outside a circle to draw a tangent to the circle.
n Given O CA and an outside point P.
To construct a tangent from P to the circle.
Construction. Draw CP. On CP as a diameter con- struct a circle, cutting the given circle in the points A and B.
Draw tlie lines PA and PB.
Then PA and PB are both tangents.
Give the proof.
231. EXERCISES.
1. If in the figure of § 2. 30 the point P is made to move towards the circle along the line PC until it finally reaches thgjcircle, while PA and PB remain tangent to the circle, describe the motion of the points A and B and also of the lines PA and PB.
What to read after Plane Geometry With Problems And Applications?
You can find similar books in the "Read Also" column, or choose other free books by H E Herbert Ellsworth Slaught to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
3. Is the construction possible when all three lines are parallel? Why?
STRAIGHT LINES AND CIRCLES. 105 4. If two sides of the triangle are produced, as AB and AD in the figure of § 227, construct a circle tangent to the side BD and to the prolongations of the sides AB and AD.
This is called an escribed circle of the triangle.
5. How many circles can be constructed tangent to each of three straight lines if they are not concurrent and no two of them are parallel?
6. Draw a triangle and construc...t its inscribed and circumscribed circles and its three escribed circles.
230. Pkoblem. From a given point outside a circle to draw a tangent to the circle.
n Given O CA and an outside point P.
To construct a tangent from P to the circle.
Construction. Draw CP. On CP as a diameter con- struct a circle, cutting the given circle in the points A and B.
Draw tlie lines PA and PB.
Then PA and PB are both tangents.
Give the proof.
231. EXERCISES.
1. If in the figure of § 2. 30 the point P is made to move towards the circle along the line PC until it finally reaches thgjcircle, while PA and PB remain tangent to the circle, describe the motion of the points A and B and also of the lines PA and PB.
What to read after Plane Geometry With Problems And Applications?
You can find similar books in the "Read Also" column, or choose other free books by H E Herbert Ellsworth Slaught to read onlineMoreLess
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