Plane and solid geometry . e intersecting the circumferenceof circle 0 in points T and V, 3. Draw P r and PK 4. PT and PFare tangents from P to circle 0. II. The proof and discussion are left as an exercise for thestudent. Hint. Draw OT and OF and apply § 367. Ex. 492. Circumscribe an isosceles triangle about a given circle, thebase of the isosceles triangle being equal to a given line. What restric-tion is there on the length of the base ? Ex. 493. Circumscribe a right triangle about a given circle, one armof the triangle being equal to a given line. What is the least lengthpossible for the g
Plane and solid geometry . e intersecting the circumferenceof circle 0 in points T and V, 3. Draw P r and PK 4. PT and PFare tangents from P to circle 0. II. The proof and discussion are left as an exercise for thestudent. Hint. Draw OT and OF and apply § 367. Ex. 492. Circumscribe an isosceles triangle about a given circle, thebase of the isosceles triangle being equal to a given line. What restric-tion is there on the length of the base ? Ex. 493. Circumscribe a right triangle about a given circle, one armof the triangle being equal to a given line. What is the least lengthpossible for the given line, as compared with the diameter of the circle ? Ex. 494. If a circumference M passes through the center of a circle5, the tangents to B at the points of intersection of the circles intersecton circumference M, Ex. 495. Circumscribe an isosceles triangle about a circle, the altitudeupon the base of the triangle being given. 150 PLANE GEOMETEY Ex. 496. Construct a common external tangent to two given circlesT • Y. Given circles MTB and NVS. To construct a common external tangent to circles MTB and N VS* I. Construction 1. Draw the line of centers OQ. 2. Suppose radius OM > radius QN. Then, with O as center andwith OL = OM— ^iYas radius, construct circle LPK. 3. Construct tangent QP from point Q to circle LPK. § 373. 4. Draw OP and prolong it to meet circumference MTR at T. 5. Draw QVWOT, § 188. 6. Draw TV. 7. TV is tangent to circles MTB and NVS. II. The proof and discussion are left as an exercise for the student. Ex. 497. Construct a second common external tangent to circles MTUand NVS by samemethod. How is themethod modified if thetwo circles are equal ? Ex. 498. Construct acommon internal tangentto two circles. Hint. Follow stepsof Ex. 406 except step OL = OM-\- QN. Ex. 499. By movingQ toward 0 in the preceding figure, show when there are four commontangents ; when only three ; when only two ; when only one ; when none.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
