PA and PB are tangents to the circle and O is the centre of the circle. The radius is 5 cm and PO is 13 cm. If the area of the triangle PAB is M, then the value √(M/15) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 24/13.
| Understanding/Application |
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In triangle OAP - OA2 + AP2 = OP2 52 + AP2 = 132 AP2 = 169 - 25 AP = 12 cm Similarly, BP = 12 cm In triangle OAP - sin x = OA/OP sin x = 5/13 cos x = AP/OP cos x = 12/13 In triangle ACP - sin x = AC/AP 5/13 = AC/12 AC = 60/13 Similarly, BC = 60/13 cos x = CP/AP 12/13 = CP/12 CP = 144/13 |
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Area of triangle PAB = M 1/2. AB. CP = M 1/2. (AC + BC). CP = M 1/2. (60/13 + 60/13). 144/13 = M 1/2 × 120/13 × 144/13 = M M = (60 × 144)/169 M/15 = (60 × 144)/(169 × 15) √(M/15) = 24/13 |