University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2021
Views:

56

Pages:

3
Author:

Accinkiquicpqw

EXERCISE # 2 Q.1 In fig. ABCD is a cyclic quadrilateral; O is the centre of the circle. If BOD = 160º, find the measure of BPD. A Q.5 [NCERT] Q.6 Q.2 (i) ACD, and (ii) CAD 160º P In the given figure, AB is a diameter of the circle and CD || AB. If DAB = 25º, calculate O D Prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic. B In fig. ABC is an isosceles triangle with AB = AC and m ABC = 50º. Find m BDC and m BEC A D A Q.7 50º B D C C C 25º B O From the given figure, find out the values of x and y, when A = (2x + 4)º, B = (x + 10)º C = (4y – 4)º and D = (5y + 5)º E Q.3 A In fig. ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C, D. If (ADC) = 130º, Find BAC. 130º C (2x+4)º B (x+10)º (5y+5)º D D (4y–4)º A B C Q.8 In the given figure, O is the centre of a circle and AOC = 140º. Find ABC. Q.4 In the given figure, ABCD is a parallelogram. The circle through A, B, C intersects CD produced at E. Prove that AD = AE. E D O 140º C C A A B B Q.9 In the given figure, O is the centre of a circle Q.13 and ADC = 130º. If BAC = xº, find the the point of their intersecton on any side when produced backwards, bisects the opposite side. value of x. 130º C D Q.14 PQ and RQ are the chords of a circle equidistant from the centre. Prove that the xº A The diagonals of a cyclic quadrilateral are at right angles. Prove that the perpendicular from O B diameter passing through Q bisects PQR and PSR. Q Q.10 In the given figure, AB is a diameter of a circle P O with centre O and CD || BA. If BAC = 20º, S R find . (i) BOC (ii) COD (iii) CAD (iv) ADC D C Q.15 In the given figure, AB is a diameter of a circle with centre O. If ADE and CBE are straight lines, meeting at E such that BAD = 35º and BED = 25º, find A (i) DBC (ii) DCB (iii) BDC. 20º B O A Q.11 Q.12 Prove that an isosceles trapezium is always cyclic. Or If two nonparallel sides of a trapezium are equal, prove that it is cyclic. In the figure, ABCD is a qudrilateral in which AD = BC and ADC = BCD. Show that the points A, B, C, D lie on a circle. A E F D C B 35º D O 25º B C E ANSWER KEY 1. 100º 2. 80º, 100º 3. 40º 6. 115º, 40 7. 40, 25 8. 110º 9. 40 10. 40º, 100º, 50º, 110º 15. 115º, 35º, 30º