Plane Geometry
- Two parallel chords of a circle of diameter 20 cm are 12 cm and 16 cm long. If the chords are in the same side of the centre, then the distance between them is
-
View Hint View Answer Discuss in Forum
According to question , we draw a figure of a circle with centre O and in which two parallel chords are AB and CD ,
OA = OC = radius = 10 cm
AB = 16 cm
CD = 12 cm
In ∆ OAE,
∠OEA = 90°
∴ AE = EB = 8 cm
∴ OE = √OA² - AE²
OE = √10² - 8² = √100 - 64
OE = √36 = 6 cm
In ∆ OFC,
∠OFC = 90°
∴ CF = FD = 6 cmCorrect Option: B
According to question , we draw a figure of a circle with centre O and in which two parallel chords are AB and CD ,
OA = OC = radius = 10 cm
AB = 16 cm
CD = 12 cm
In ∆ OAE,
∠OEA = 90°
∴ AE = EB = 8 cm
∴ OE = √OA² - AE²
OE = √10² - 8² = √100 - 64
OE = √36 = 6 cm
In ∆ OFC,
∠OFC = 90°
∴ CF = FD = 6 cm
∴ OF = √OC² - OF²
OF = √10² -6²
OF = √100 - 36
OF = √64 = 8 cm
∴ Required distance = EF = OF – OE
Required distance = 8 – 6 = 2 cm
- Two circles with centres A and B of radii 5 cm and 3 cm respectively touch each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, then the value of PQ is
-
View Hint View Answer Discuss in Forum
As per the given in question , we draw a figure of two circles with centres A and B of radii 5 cm and 3 cm respectively touch each other internally ,
In ∆ PBE,
PB = 5 cm
BE = 1 cm
PE = √PB² - BE²Correct Option: D
As per the given in question , we draw a figure of two circles with centres A and B of radii 5 cm and 3 cm respectively touch each other internally ,
In ∆ PBE,
PB = 5 cm
BE = 1 cm
PE = √PB² - BE²
PE = √25 - 1 = √24 = 2√6 cm
∴ PQ = 2PE = 4√6 cm
- Two circles having radii r units intersect each other in such a way that each of them passes through the centre of the other. Then the length of their common chord is
-
View Hint View Answer Discuss in Forum
According to question , we draw a figure of two circles with centres C and D ,
CO = OD = r units 2
AC = r units
In ∆ AOC,
OA = √AC² - OC²= √ r² - r² = √ 3r² = √3r 4 4 2
Correct Option: B
According to question , we draw a figure of two circles with centres C and D ,
CO = OD = r units 2
AC = r units
In ∆ AOC,
OA = √AC² - OC²= √ r² - r² = √ 3r² = √3r 4 4 2 ∴ AB = 2OA = 2 × √3r 2
AB = √3r units
- Two circles intersect each other at the points A and B, A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is
-
View Hint View Answer Discuss in Forum
As per the given in question , we draw a figure of two circles intersect each other at the points A and B, A straight line parallel to AB intersects the circles at C, D, E
Correct Option: C
As per the given in question , we draw a figure of two circles intersect each other at the points A and B, A straight line parallel to AB intersects the circles at C, D, E
Clearly, CD = EF = = 4.5 cm.
- Chords AC and BD of a circle with centre O intersect at right angles at E. If ∠OAB = 25°, then the value of ∠EBC is
-
View Hint View Answer Discuss in Forum
According to question , we draw a figure of a circle with centre O ,
From figure , OA = OB = radii
∠OAB = ∠OBA = 25°
∴ ∠AOB = 180° – 50° = 130°Correct Option: B
According to question , we draw a figure of a circle with centre O ,
From figure , OA = OB = radii
∠OAB = ∠OBA = 25°
∴ ∠AOB = 180° – 50° = 130°∴ ∠BCA = 130° = 65° 2
∴ ∠EBC = 90° – 65° = 25°
