Plane Geometry
- Two circles with their centres at O and P and radii 8 cm and 4 cm respectively touch each other externally. The length of their common tangent is
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We know that , Common tangent = √(Direct between centres)² - (r1 - r2)²
Common tangent = √(8 + 4)² - (8 - 4)²
Common tangent = √12² - 4²Correct Option: C
We know that , Common tangent = √(Direct between centres)² - (r1 - r2)²
Common tangent = √(8 + 4)² - (8 - 4)²
Common tangent = √12² - 4²
Common tangent = √144 - 16 = √128
Common tangent = 8√2 cm
- In the given figure, PAB is a secant and PT is a tangent to the circle from P. If PT = 5 cm, PA = 4 cm and AB = x cm, then x is
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From the given figure in question ,
Given , PT = 5 cm, PA = 4 cm and AB = x cm,
Secant PB = (4 + x) cm.
As we know that ,
∴ PA. PB = PT²
⇒ 4 (4 + x) = 5² = 25
⇒ 16 + 4x = 25Correct Option: B
From the given figure in question ,
Given , PT = 5 cm, PA = 4 cm and AB = x cm,
Secant PB = (4 + x) cm.
As we know that ,
∴ PA. PB = PT²
⇒ 4 (4 + x) = 5² = 25
⇒ 16 + 4x = 25
⇒ 4x = 25 – 16 = 9⇒ x = 9 cm. 4
- The distance between the centres of two circles having radii 8 cm and 3 cm, is 13 cm. The length (in cm) of the direct common tangent of the two circles is
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As per the given in question , we draw a figure of two circles having radii 8 cm and 3 cm
As we know that , Length of direct common tangent = √(Distance between two centres)² - (r1 - r2)²
Length of direct common tangent = √13² - (8 - 3)²
Length of direct common tangent = √13² - 5²Correct Option: D
As per the given in question , we draw a figure of two circles having radii 8 cm and 3 cm
As we know that , Length of direct common tangent = √(Distance between two centres)² - (r1 - r2)²
Length of direct common tangent = √13² - (8 - 3)²
Length of direct common tangent = √13² - 5²
Length of direct common tangent = √(13 + 5)(13 - 5)
Length of direct common tangent = √18 × 8 = 12 cm
- AB is a diameter of a circle with centre O. The tangents at C meets AB produced at Q. If∠CAB = 34°, then measure of ∠CBA is
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According to question , we draw a figure of a circle with centre O ,
The angle at the circumference of a semi–circle is right angle.Correct Option: A
According to question , we draw a figure of a circle with centre O ,
The angle at the circumference of a semi–circle is right angle.
∴ ∠ ACB = 90° ∠ CAB = 34°
∴ ∠ CBA = 90° – 34° = 56°
- If two circles of radii 9 cm and 4 cm touch externally, then the length of a common tangent is
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As per the given in question , we draw a figure of two circles of radii 9 cm and 4 cm touch externally
OO' = r1 + r2 = 9 + 4 = 13 cm
∴ Common tangent = √(r1 + r2)² - (r1 - r2)²
Common tangent = √13² - (9 - 4)²Correct Option: D
As per the given in question , we draw a figure of two circles of radii 9 cm and 4 cm touch externally
OO' = r1 + r2 = 9 + 4 = 13 cm
∴ Common tangent = √(r1 + r2)² - (r1 - r2)²
Common tangent = √13² - (9 - 4)²
Common tangent = √13² - 5² = √169 - 25
Common tangent = √144 = 12 cm
