Two circles of radii 10 cm and 8 cm intersect at the points P and Q. If PQ = 12 cm, and the distance between the centres of the circles is x cm. The value of x (correct to one decimal place) is:
Show answer & explanation
Correct answer: C
Explanation
Correct Answer is option 3 i.e. 13.3
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Concept |
Understanding |
Application |
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The tangent to a circle is always perpendicular to the radius. Use Pythagoras Theorem. |
Given OP = 8 cm, O’P = 10 cm, PQ = 12 cm and PM = 6 cm
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In ΔPOM By using Pythagoras Theorem ⇒ (OP)2 = (OM)2 + (PM)2 ⇒ 82 = (OM)2 + 62 ⇒ (OM)2 = 64 – 36 = 28 ⇒ OM = √28 cm In ΔPO’M By using Pythagoras Theorem ⇒ (O’P)2 = (O’M)2 + (PM)2 ⇒ 102 = (O’M)2 + 62 ⇒ (O’M)2 = 100 – 36 = 64 ⇒ O’M = 8 cm ⇒ O’O = OM + O’M = √28 + 8 = 5.3 + 8 = 13.3 cm |
