Plane Geometry
- If PA and PB are two tangents to a circle with centre O such that ∠APB = 80°, then, ∠AOP = ?
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According to question , we draw a figure of a circle with centre O
OA ⊥ PA ; OB ⊥ PB : PA = PB
(tangents from the same external point)
∠APB = 80° : OA = OB = radiusCorrect Option: B
According to question , we draw a figure of a circle with centre O
OA ⊥ PA ; OB ⊥ PB : PA = PB
(tangents from the same external point)
∠APB = 80° : OA = OB = radius∴ ∠APO = 80° = 40° 2
∴ ∠AOP = 90° – 40° = 50°.
- The distance between centres of two circles of radii 3 cm and 8 cm is 13 cm. If the points of contact of a direct common tangent to the circles are P and Q, then the length of the line segment PQ is :
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As per the given in question , we draw a figure of two circles of radii 3 cm and 8 cm
Given that , OO' = 13 cm
PQ = √(OO')² - (r2 - r1)²
PQ = √(13)² - (8 - 3)²Correct Option: B
As per the given in question , we draw a figure of two circles of radii 3 cm and 8 cm
Given that , OO' = 13 cm
PQ = √(OO')² - (r2 - r1)²
PQ = √(13)² - (8 - 3)²
PQ = √169 - 25
PQ = √144 = 12 cm.
- Two circles of radii 5 cm and 3cm touch externally, then the ratio in which the direct common tangent to the circles divides externally the line joining the centers of the circles is:
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According to question , we draw a figure of two circles with radii 5 cm and 3cm touch externally
Given that , Two circles of radii are 5 cm and 3cmCorrect Option: A
According to question , we draw a figure of two circles with radii 5 cm and 3cm touch externally
Given that , Two circles of radii are 5 cm and 3cmRequired ratio = r1 = 5 : 3 r2
- The distance between the centres of two circles of radii 6 cm and 3 cm is 15 cm. The length of the transverse common tangent to the circles is :
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As per the given in question , we draw a figure of two circles of radii 6 cm and 3 cm
Here , Direct between centres = 15 cm
Length of common transverse tangent = √(Direct between centres)² - (r1 + r2)²
Length of common transverse tangent = √15² - (6 + 3)²Correct Option: A
As per the given in question , we draw a figure of two circles of radii 6 cm and 3 cm
Here , Direct between centres = 15 cm
Length of common transverse tangent = √(Direct between centres)² - (r1 + r2)²
Length of common transverse tangent = √15² - (6 + 3)²
Length of common transverse tangent = √225 - 81
Length of common transverse tangent = √144 = 12 cm.
- AB and AC are tangents to a circle with centre O. A is the external point of the circle. The line AO intersect the chord BC at D. The measure of the ∠BDO is
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On the basis of question we draw a figure of a circle with centre O ,
AB = AC = tangents drawn from an exterior pointCorrect Option: B
On the basis of question we draw a figure of a circle with centre O ,
AB = AC = tangents drawn from an exterior point
D is mid-point of BC and AD is perpendicular to BC.
∴ ∠BDO = 90°
