Topics

General Knowledge
General Science
General English
Aptitude
General Computer Science
General Intellingence and Reasoning
Current Affairs
Exams
Elementary Mathematics
English Literature

Chords AB and CD of a circle intersect at O. If AO = 8 cms, BO = 9 cms and CO = 2 DO, then length of DO (in cms) is

A) 5.67 approx.
B) 5
C) 6
D) 6.17 (approx)

Correct Answer:



C) 6

Description for Correct answer:

Let OD = x cm, then OC = 2x

From Geometry, if two chords of a circle intersect then

Therefore, \( \Large OC \times OD = OA \times OB \)

=> \( \Large 2x \times x = 8 \times 9 \)

=> or \( \Large x^{2} = 36 \)

=> x = 6

Part of solved Loci and concurrency questions and answers : >> Elementary Mathematics >> Loci and concurrency

Comments

Similar Questions

1). If A, B be points of contact of the tangents drawn to a circle C with centre O and radius r cm from a point P Outside C, then which one of the following is correct ?

A). If M is mid-point of AB, then OM + MP > OP.

B). If M is mid-point of AB, then AMP is an acute angled triangle.

C). If M is mid-point of AB, then AM is perpendicular to OP.

D). Either \( \Large \triangle AOP \) is obtuse-angled or \( \Large \triangle BOP \) is obtuse-angled.

2). If C be a circle with centre O and radius 5 cm, then locus of mid-points of equal chords of C each of length 6 cm is a

A). concentric circle whose radius is 7 cm.

B). concentric circle whose radius is 4 cm.

C). straight line parallel to some chord of length of 6 cm.

D). straight line perpendicular to some chord of length of 6 cm.

3). If area of circle is 13.86 hectares, then cost of fencing it at the rate of 60 paise per metre is

A). Rs.784.00

B). Rs.788.00

C). Rs.792.00

D). Rs.796.00

4). If chords AP and AQ of a circle of radius 6 cm are at distance 3 cm and \( \Large 3\sqrt{2} \) cm respectively from the centre O of the circle, then area of the smaller sector POQ is

A). \( \Large 24 \pi cm^{2} \)

B). \( \Large 21 \pi cm^{2} \)

C). \( \Large 15 \pi cm^{2} \)

D). \( \Large 12 \pi cm^{2} \)

5). If C be a circle with centre O and radius x cm, then locus of midpoints of equal chords of C each of length y cm will be

A). a circle with centre O and radius \( \Large \frac{1}{2}\sqrt{4x^{2}+y^{2}} cm \)

B). a circle with centre O and radius \( \Large \frac{1}{2}\sqrt{4x^{2}-y^{2}} cm \)

C). diameter of the circle C

D). a circle with centre O and radius \( \Large \frac{1}{2}\sqrt{4x^{2}-x^{2}} cm \)

6). The straight lines AB and CD intersect at E. If EF and EG are bisectors of \( \Large \angle DEA\ and\ \angle AEC \) respectively and if \( \Large \angle AEF = x\ and\ \angle AEG = y \), then

A). \( \Large x + y > 90 ^{\circ} \)

B). \( \Large x + y < 90 ^{\circ} \)

C). \( \Large x + y = 90 ^{\circ} \)

D). \( \Large x + y = 180 ^{\circ} \)

7). If AB is parallel to CD in the given figure, then \( \Large \angle x,\ \angle y\ and\ \angle z \) respectively are

A). \( \Large 60 ^{\circ} , 50 ^{\circ} ,\ 70 ^{\circ} \)

B). \( \Large 50 ^{\circ} , 60 ^{\circ} ,\ 70 ^{\circ} \)

C). \( \Large 60 ^{\circ} , 60 ^{\circ} ,\ 60 ^{\circ} \)

D). \( \Large 70 ^{\circ} , 50 ^{\circ} ,\ 60 ^{\circ} \)

8). A line parallel to BC in \( \Large \triangle ABC \) meets AB. AC in D and E respectively. If \( \Large AD= \left(4x-3\right)cm, \) \( \Large DB= \left(3x-1\right)cm,\) \( \Large AE= \left(8x-7\right)cm\ and\ EC= \left(5x-3\right)cm \), then admissible value of x is

A). 0

B). 1

C). 2

D). 3

9). If radius of a circle is increased by 75%, then its circumference will increase by

A). 50%

B). 75%

C). 25%

D). 100%

10). The earth makes a complete revolution about its axis in 24 hours. The angle through which it will turn in 4 hours and 40 minutes, is equal to

A). \( \Large 50 ^{\circ} \)

B). \( \Large 60 ^{\circ} \)

C). \( \Large 70 ^{\circ} \)

D). \( \Large 120 ^{\circ} \)