A is a point at a distance 26 cm from the centre O of a circle of radius 10 cm. AP and AQ are the tangents to the circle at the point of contracts P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, then the perimeter of ΔABC is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 48 cm
| Understanding | Application |
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The length of tangents drawn from an external point to a circle is equal. The Pythagoras theorem states that the sum of squares of perpendicular and base of the right-angle triangle is equal to the square of the hypotenuse. |
⇒ BP = BR and CR = CQ Perimeter of ∆ABC = AB + BR + RC +AC ⇒ AB + BP + QC + CA We know that AP = QA ⇒ AP + QA = 2AP ⇒ AO2 = AP2 + PO2 ⇒ AP = √(676 - 100) ⇒ 24 cm Perimeter of ABC = 2AP ⇒ 2 × 24 = 48 cm |