Mathematics
Assertion (A): In the figure, AB, AC and DE are tangents to the circle. If AC = 7 cm, then perimeter of ΔADE is 14 cm.
Reason (R): The lengths of tangents to a circle from an exterior point are 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
The lengths of tangents to a circle from an exterior point are equal.
∴ Reason (R) is true.
∴ AB = AC = 7 cm
⇒ Perimeter of ΔADE = AD + AE + DE
We can write DE as (DP + PE)
⇒ Perimeter of ΔADE = AD + AE + (DP + PE)
Substituting DP with DB and PE with EC:
⇒ Perimeter of ΔADE = AD + AE + (DB + EC)
⇒ Perimeter of ΔADE = (AD + DB) + (AE + EC)
⇒ Perimeter of ΔADE = AB + AC
⇒ Perimeter of ΔADE = 7 + 7
⇒ Perimeter of ΔADE = 14 cm.
Assertion (A) is true.
Hence, option 3 is the correct option.
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