Mathematics
Assertion (A) : In the figure below, CD = 7.8 cm, PD = 5 cm, PB = 4 cm, then PT = 8 cm.
Reason (R) : If two chords of a circle intersect internally or externally then the product of the lengths of their segments is equal.
A is true, R is false.
A is false, R is true.
Both A and R are true.
Both A and R are false.
Circles
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Answer
We know that,
If a chord and a tangent intersect externally, then the product of the lengths of the segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
⇒ PT2 = PC × PD
⇒ PT2 = (PD + CD) × PD
⇒ PT2 = (5 + 7.8) × 5
⇒ PT2 = 12.8 × 5
⇒ PT2 = 64
⇒ PT = = 8 cm.
∴ Assertion (A) is true.
We know that,
If two chords of a circle intersect internally or externally then the product of the lengths of their segments is equal.
∴ Reason (R) is true.
Hence, Option 3 is the correct option.
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