Plane Geometry
- A vertical stick 12 cm long casts a shadow 8 cm long on the ground. At the same time a tower casts the shadow 40 m long on the ground. Find the height of the tower.
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Draw a figure as per given question,
In ΔACB and PCQ
∠C = ∠C (common)
∠ABC = ∠PQC (each 90°)
∴ ΔACB ∼ ΔPC (AA Similarity)
Correct Option: C
In ΔACB and PCQ
∠C = ∠C (common)
∠ABC = ∠PQC (each 90°)
∴ ΔACB ∼ ΔPC (AA Similarity)∴ AB = BC PQ QC h = 4000 12 8
h = 60m
- If angles of measure (5y + 62°) and (22° + y) are supplementary, then value of y is :
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As we know that Sum of two supplementary angles = 180°
∴ ( 5y + 62° ) + ( 22° + y ) = 180°
⇒ 6y + 84° = 180°
⇒ 6y = 180° – 84° = 96°Correct Option: A
As we know that Sum of two supplementary angles = 180°
∴ ( 5y + 62° ) + ( 22° + y ) = 180°
⇒ 6y + 84° = 180°
⇒ 6y = 180° – 84° = 96°∴ y = 96 = 16° 6
- ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120° and ∠BAC = 30°, then ∠BCD is :
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As per the given in question , we draw a figure of a quadrilateral ABCD inscribed in a circle with centre O
Given , ∠COD = 120°
∠BAC = 30°∠CAD = 1 × ∠COD 2 ∠CAD = 1 × 120° = 60° 2
Correct Option: B
As per the given in question , we draw a figure of a quadrilateral ABCD inscribed in a circle with centre O
Given , ∠COD = 120°
∠BAC = 30°∠CAD = 1 × ∠COD 2 ∠CAD = 1 × 120° = 60° 2
∴ ∠BAD = 90°
∴ ∠BCD = 180° - ∠BAD
∴ ∠BCD = 180° – 90° = 90°
- The radius of two concentric circles are 9 cm and 15 cm. If the chord of the greater circle be a tangent to the smaller circle, then the length of that chord is
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According to question , we draw a figure of a circle with centre O ,
Here , BO = OC = 15 cm and OD = 9 cm.
From ∆ BDO ,
∴ BD = √BO² - OD²Correct Option: A
According to question , we draw a figure of a circle with centre O ,
Here , BO = OC = 15 cm and OD = 9 cm.
From ∆ BDO ,
∴ BD = √BO² - OD²
∴ BD = √15² - 9²
BD = √24 × 6 = 12 cm
∴ BC = 2 × 12 = 24 cm.
- The distance between the centres of the two circles of radii r1 and r2 is d. They will touch each other internally if
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According to question , we can draw a figure
Correct Option: C
According to question , we can draw a figure
Hence , option C is correct answer .