YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …
Transcript of YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …
![Page 1: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/1.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
NAME : 52 marks
Page 1 PLEASE TURN OVER
QUESTION 1 Find x in the following diagrams giving reasons. (a)
(2 marks)
(b)
(2 marks) (c)
(3 marks) (d)
(3 marks)
![Page 2: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/2.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 2
(e)
(3 marks)
(f)
(3 marks)
(g)
(2 marks)
![Page 3: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/3.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 3 PLEASE TURN OVER
(h)
(4 marks)
(i)
(3 marks)
(j)
(2 marks)
![Page 4: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/4.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 4
QUESTION 2
PV is a tangent to the circle and QRST is a cyclic quadrilateral.
Prove that PV is parallel to QT.
(4 marks)
QUESTION 3
ABCD is a quadrilateral. Diagonals AC and BD intersect at E.
If AC bisects and , prove that ABCD is a cyclic quadrilateral.
(3 marks)
![Page 5: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/5.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 5 PLEASE TURN OVER
QUESTION 4
Triangle PQR is inscribed in a circle with PR as a diameter. The perpendicular from P to the
tangent at Q meets the tangent at S, prove that PQ bisects .
(4 marks)
QUESTION 5
OABC is a parallelogram. A circle, centre at O and radius OA is drawn. BA produced meets the
circle at D. Prove that DOCB is a cyclic quadrilateral.
(5 marks)
![Page 6: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/6.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 6
QUESTION 6
Triangle ABC has perpendiculars CX and BY as shown.
(a) What can be said about quadrilaterals AXOY and BXYC? Give reasons.
(2 marks)
(b) Prove that .
(2 marks)
![Page 7: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/7.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 7 PLEASE TURN OVER
(c) Prove that AZ is perpendicular to BC.
(2 marks)
![Page 8: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/8.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 8
QUESTION 7
RX is the bisector of . Prove that PX bisects .
(3 marks)
![Page 9: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/9.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 9 PLEASE TURN OVER
QUESTION 1 Find x in the following diagrams giving reasons. (a)
(2 marks)
(b)
(2 marks)
(c)
(3 marks)
(d)
(3 marks)
![Page 10: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/10.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 10
(e)
(3 marks)
(f)
(3 marks)
(g)
(2 marks)
![Page 11: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/11.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 11 PLEASE TURN OVER
(h)
(4 marks)
(i)
(3 marks)
(j)
(2 marks)
![Page 12: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/12.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 12
QUESTION 2
PV is a tangent to the circle and QRST is a cyclic quadrilateral.
Prove that PV is parallel to QT.
(4 marks)
QUESTION 3
ABCD is a quadrilateral. Diagonals AC and BD intersect at E.
If AC bisects and , prove that ABCD is a cyclic quadrilateral.
(3 marks)
![Page 13: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/13.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 13 PLEASE TURN OVER
QUESTION 4
Triangle PQR is inscribed in a circle with PR as a diameter. The perpendicular from P to the
tangent at Q meets the tangent at S, prove that PQ bisects .
(4 marks)
QUESTION 5
OABC is a parallelogram. A circle, centre at O and radius OA is
drawn. BA produced meets the circle at D.
Prove that DOCB is a cyclic quadrilateral.
(5 marks)
![Page 14: YEAR 11 SPECIALIST MATHEMATICS GEOMETRY NAME : 52 …](https://reader031.fdocuments.net/reader031/viewer/2022011805/61d3ac6693e1280f22519073/html5/thumbnails/14.jpg)
YEAR 11 SPECIALIST MATHEMATICS GEOMETRY
Page 14
QUESTION 6
Triangle ABC has perpendiculars CX and BY as shown.
(a) What can be said about quadrilaterals AXOY and BXYC? Give reasons.
(2 marks)
(b) Prove that .
(2 marks)
(c) Prove that AZ is perpendicular to BC.
(2 marks)
QUESTION 7
RX is the bisector of . Prove that PX bisects .
(3 marks)