PA and PB are two tangents drawn to two circles of radius 3 cm and 5 cm respectively. PA touches the smaller and larger circles at points X and Y respectively. PB touches the smaller and large circle at point U and V respectively. The centres of the smaller and larger circles O and N respectively. If ON =12 cm, then what is the value (in cm) of PY?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 5√35
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Application |
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In the figure; Let PO = a cm Triangle POX and triangle PNY are similar. ∴ PO/PN = XO/YN ⇒ a/(a + 12) = 3/5 ⇒ 5a = 3a + 36 ⇒ a = 18 ∴ PN = 18 + 12 = 30 cm Triangle PNY is a right angle triangle (Since PY is the tangent to the circle); ∴ (PN)2 = PY2 + YN2 ⇒ PY2 = 302 – 52 ⇒ PY2 = 875 ∴ PY = 5√35 cm |
