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/ 57.TA, TB are tangents to a circle with centre o. ChordAB intersects TO at C.Giventofind AB1.8cm2. 12cm3.9cm4.4cm |
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Answer» 1/(OA)² + 1/(TA)² = 1/36 Multiply both sides by (OA)² (TA)²(TA)² + (OA)² = (OA)² (TA)² / 36 Since TA is a tangent of the circle, then TA is perpendicular to OA, so △OAT has a right angle at A. By Pythagorean theorem:(TA)² + (OA)² = (OT)² Therefore:(OT)² = (OA)² (TA)² / 36OT = OA * TA / 6 AB is perpendicular to OT. Therefore, AC is perpendicular to OTSince △OAT is a right triangle, dropping perpendicular from right angle A to side OT (at C) creates 2 right triangles that are both similar to △OAT △OAT ~ △OCA ~ △ACT By similar triangles:AC/OA = TA/OTAC = OA * TA / OTAC = OA * TA / (OA * TA / 6)AC = 6 AB = 2 * ACAB = 12 Option 2) 12 cm is correct. |
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