AB is a chord of length 32 cm of a circle of radius 20 cm, the tangents at A and B intersect at a point T. Find length TA (rounded off to two digits after decimal).
AB is a chord of length 32 cm of a circle of radius 20 cm, the tangents at A and B intersect at a point T. Find length TA (rounded off to two digits after decimal).
AB 20 सेमी त्रिज्या वाले एक वृत्त की 32 लंबी जीवा है। A और B की स्पर्श रेखाएँ बिंदु T पर प्रतिच्छेद करती हैं। लंबाई TA ज्ञात कीजिए। ( दशमलव के बाद दो अंक तक पूर्णांकित।)
Detailed Solution & Logic
Correct Answer:
26.67 cm 4
OA=OB=20 cm, AB=32 cm$
$AM=\dfrac{32}{2}=16\text{ cm}$
$OM=\sqrt{20^2-16^2}=\sqrt{400-256}=12\text{ cm}$
$\triangle OMT\sim\triangle OAT$
$\dfrac{12}{20}=\dfrac{20}{OT}$
$OT=\dfrac{100}{3}$
$TA=\sqrt{\left(\dfrac{100}{3}\right)^2-20^2}=\dfrac{80}{3}=26.67\text{ cm}$
Answer = 26.67 cm
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