In the given figure, MP is tangent to a circle with centre A and NQ is a tangent to a circle with centre B. If MP = 15 cm, NQ = 8 cm. PA = 17 cm and BQ = 10 cm, then AB is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 14 cm
| Understanding/Application |
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MP is tangent to the circle with center A. So, MP is perpendicular to AM. From, triangle PAM - AM2 + MP2 = PA2 ⇒ AM2 + 152 = 172 ⇒ AM2 = 64 ⇒ AM = 8 cm Radius of the larger circle = AC = AM = 8 cm |
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NQ is tangent to the circle with center B. So, NQ is perpendicular to BN. From, triangle QBN - BN2 + NQ2 = BQ2 ⇒ BN2 + 82 = 102 ⇒ BN2 = 36 ⇒ BN = 6 cm Radius of the smalller circle = BC = BN = 6 cm AB = AC + BC = 8 + 6 = 14 cm |