...polygon. Prove that every equiangular polygon circumscribed about a circle is a regular polygon. 5. Prove that the opposite angles of a quadrilateral inscribed in a circle are supplements of each other. 6. Construct a square, having given its diagonal. 7. Prove that the area...

...polygon. Prove that every equiangular polygon circumscribed about a circle is a regular polygon. 5. Prove that the opposite angles of a quadrilateral inscribed in a circle are supplements of each other. 6. Construct a square, having given its diagonal. 7. Prove that the area...

...perpendiculars from the angles of a triangle to the opposite sides meet in a point (4 marks). 2. Prove that the opposite angles of a quadrilateral inscribed in a circle are equal to two right angles (10 marks). Show also that if a circle be inscribed in this quadrilateral...

...polygon. Prove that every equiangular polygon circumscribed about a circle is a regular polygon. 5. Prove that the opposite angles of a quadrilateral inscribed in a circle are supplements of each other. 6. Construct a square, having given its diagonal. 7. Prove that the area...

...part of it produced beyond the obtuse angle to meet a perpendicular from the opposite vertex. 16. 7. The opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. Two circles have a common chord AB, and from A straight lines APQ, АП8 are drawn cutting the circles...

...with equal vertical angles is an arc of a circle. PKOPOSITION 22. THEOREM. The opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. Let ABCD be a quadrilateral inscribed in the 0 ABC. Then shall (i) the L? ADC, ABC together = two rt....

...triangle the square on the hypotenuse is equali 17 to the sum of the squares on the other two sides. i 3. The opposite angles of a quadrilateral inscribed in a circle are together' 17 equal to two right angles. 42 iii 64 VICTORIA, A. 1901 4. Construct an isosceles triangle having...

...is at right angles to the diameter of the circle through its point of contact. 7. Show that any two opposite angles of a quadrilateral inscribed in a circle are together equal to two right angles. Show that two opposite sides of a convex quadrilateral (ie , a quadrilateral without re.entrant angles)...

...ABC and DEF are mutually equiangular. Prove that they are similar. Take eit)tcr 5 or &• 5. Prove that the opposite angles of a quadrilateral inscribed in a circle are supplementary. 6. Let there be a regular inscribed polygon whose number of sides is indefinitely increased....

...another in only one point, . whether it touch it internally or externally. 4. The opposite angles of any quadrilateral inscribed in a circle are together equal to two right angles. 6. Inscribe a circle in a regular pentagon. 6. Describe a circle about a given triangle. SECTION B....