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Equal Chords

In the figure...

Question

In the figure, O is the center of the circle of radius 5 cm. P and Q are points on chords AB and CD such that OP $⊥$ AB, OQ $⊥$ CD, AB || CD, AB = 6 cm and CD = 8 cm. Determine PQ.

5 cm

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6 cm

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7 cm

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8 cm

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Solution

The correct option is C
7 cm

AP = 3 cm

CQ = 4 cm

OA = OC = Radius = 5 cm

OP = $\sqrt{({O A}^{2}) - ({A P}^{2})}$

OP = 4 cm

Similarly, OQ = 3 cm

Therefore PQ = 7 cm.

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Similar questions

Q. In fig 4.41 chord AB || chord CD of a circle with centre O and radius 5 cm such that AB = 6cm and CD = 8cm, if OP

⊥

AB, OQ

⊥

CD, Determine PQ.

O is the centre of the circle of radius 5 cm, OP is perpendicular to AB, OQ is perpendicular to CD, AB || CD, AB = 6 cm and CD = 8 cm. Determine PQ.

Q. In the figure,

O

is the centre of the circle of radius

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Q

are points on chords

A B

and

C D

respectively such that

O P ⊥ A B, O Q ⊥ C D, A B | | C D, A B = 6 cm

and

C D = 8 c m .

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Q. In the given figure,

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is the centre of a circle of radius

r

cm,

O P

and

O Q

are perpendiculars to

P Q = 1 c m

, If

A B ∥ C D, A B = 6 c m

and

C D = 8 c m

, then determine r

In the given figure, O is the centre of the circle with radius 5 cm. OP and OQ are perpendiculars to AB and CD respectively. AB = 8 cm and CD = 6 cm. Determine the length of PQ.

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In the figure, O is the center of the circle of radius 5 cm. P and Q are points on chords AB and CD such that OP ⊥ AB, OQ ⊥ CD, AB || CD, AB = 6 cm and CD = 8 cm. Determine PQ.

The correct option is C 7 cm AP = 3 cm CQ = 4 cm OA = OC = Radius = 5 cm OP = √(OA2)−(AP2) OP = 4 cm Similarly, OQ = 3 cm Therefore PQ = 7 cm.

In the figure, O is the center of the circle of radius 5 cm. P and Q are points on chords AB and CD such that OP $⊥$ AB, OQ $⊥$ CD, AB || CD, AB = 6 cm and CD = 8 cm. Determine PQ.

The correct option is C
7 cm

AP = 3 cm

CQ = 4 cm

OA = OC = Radius = 5 cm

OP = $\sqrt{({O A}^{2}) - ({A P}^{2})}$

OP = 4 cm

Similarly, OQ = 3 cm

Therefore PQ = 7 cm.