## Responsions Papers in Stated Subjects (exclusive of Books), 1901-1906: With Answers to Mathematical Questions and Introduction |

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Results 1-5 of 13

Page 65

6 . A finite straight line AB is bisected at C , and P is any external point . Prove

that ( a ) PA ? + PB2 = 2 PC2 + 2 AC2 ; ( 6 ) PA + PB is not less than 2 PC . 7 .

Show how to

that ...

6 . A finite straight line AB is bisected at C , and P is any external point . Prove

that ( a ) PA ? + PB2 = 2 PC2 + 2 AC2 ; ( 6 ) PA + PB is not less than 2 PC . 7 .

Show how to

**draw**the two tangents to a circle from an external point , and provethat ...

Page 66

Two circles intersect in the points A , B . Show how to

both circles , and prove that the middle point of the distance between the points of

contact lies on the straight line AB . III . TRINITY TERM , 1905 . 1 . ( 6 ) Show ...

Two circles intersect in the points A , B . Show how to

**draw**a straight line to touchboth circles , and prove that the middle point of the distance between the points of

contact lies on the straight line AB . III . TRINITY TERM , 1905 . 1 . ( 6 ) Show ...

Page 67

What are the cases in which ( 1 ) no such circle can be drawn ; ( 2 ) an indefinite

number of such circles can be drawn ? IV . SEPTEMBER , 1905 . 2 . A is a fixed

point in a straight line AB ; P is a point outside the line AB ; show how to

What are the cases in which ( 1 ) no such circle can be drawn ; ( 2 ) an indefinite

number of such circles can be drawn ? IV . SEPTEMBER , 1905 . 2 . A is a fixed

point in a straight line AB ; P is a point outside the line AB ; show how to

**draw**a ... Page 143

RtZ BAC = sum of Zs ABC , ACB ( I . 32 ) . But Z BAD = LDBA ( I . 5 ) . . LDAC =

LDCA , and DC = DA = DB . 4 . ( 6 ) ( See H . and S . , p . 104 . ) The rectangle

DBCE = 2 A ABO . Bisect BC at G , and

A ...

RtZ BAC = sum of Zs ABC , ACB ( I . 32 ) . But Z BAD = LDBA ( I . 5 ) . . LDAC =

LDCA , and DC = DA = DB . 4 . ( 6 ) ( See H . and S . , p . 104 . ) The rectangle

DBCE = 2 A ABO . Bisect BC at G , and

**draw**GH | | to BD . The rectangle DBGH =A ...

Page 144

( 6 ) Find centre of circle , and

line . This will meet circle at points of contact of tangents required . 8 . ( 6 ) Let AB

produced meet tangent at C in Q . ( 1 ) If Ċ and P are on the same side of Q , let

BP ...

( 6 ) Find centre of circle , and

**draw**through it diameter at right angles to givenline . This will meet circle at points of contact of tangents required . 8 . ( 6 ) Let AB

produced meet tangent at C in Q . ( 1 ) If Ċ and P are on the same side of Q , let

BP ...

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### Common terms and phrases

active ages angle base bisected Book cent centre circle contains cost decimal described difference Divide draw drawn English equal examination Express feet field Find the square Find the value fixed four fraction gain Give given Greek half HILARY TERM income indic interest invested Join king Latin locus meaning meet MICHAELMAS TERM middle point miles minutes Multiply Oratio pass perf pers person plur plural present produce propositions Prove quae quam receive Reduce respectively SEPTEMBER share shillings Show sides Simplify sing singular Solve the equations square root straight line subjunctive taken tangents Translate triangle TRINITY TERM Turn twice whole wide yards γάρ δε και μεν ου προς τε

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Page 73 - Find the locus of a point which moves so that the sum of its distances from two vertices of an equilateral triangle shall equal its distance from the third. 144. Find the locus of a point which moves so that the sum of the squares of the distances from two given points is fixed.

Page 99 - ... invidiamque eam sua sponte gliscentem insignis unius calamitas accendit. Magno natu quidam cum omnium malorum suorum insignibus se in forum proiecit. Obsita erat squalore vestis, foedior corporis Habitus pallore ac macie perempti; ad hoc promissa barba et capilli efferaverant speciem oris.

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