Question

O is the centre of circle R is external point to the circle from point R, seg RM and seg RN are tangent segments touching the circle at M and N.If OR=10 cm and radius of circle is 5 cm then,find length of each tangent segments O हे वर्तुळ केंद्र असून R हा वर्तुळाबाहेरील बिंदू आहे. रेख RM व रेख RN ह्या स्पर्शिका वर्तुळाला अनुक्रमे M व N बिंदूत छेदतात . जर OR=10 सेमी आणि वर्तुळाची त्रिज्या 5 सेमी असेल तर प्रत्येक स्पर्शिका खंडाची लांबी किती ? *



15 cm

10√3 cm

5√3 cm

25 cm

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Answer 1

Step-by-step explanation:

(1) It is given that line AB is tangent to the circle at A.

∴ ∠CAB = 90º (Tangent at any point of a circle is perpendicular to the radius throught the point of contact)

Thus, the measure of ∠CAB is 90º.

(2) Distance of point C from AB = 6 cm (Radius of the circle)

(3) ∆ABC is a right triangle.

CA = 6 cm and AB = 6 cm

Using Pythagoras theorem, we have

BC2=AB2+CA2⇒BC=62+62−−−−−−√ ⇒BC=62–√ cm

Thus, d(B, C) = 62–√ cm

(4) In right ∆ABC, AB = CA = 6 cm

∴ ∠ACB = ∠ABC (Equal sides have equal angles opposite to them)

Also, ∠ACB + ∠ABC = 90º (Using angle sum property of triangle)

∴ 2∠ABC = 90º

⇒ ∠ABC = 90°2 = 45º

Thus, the measure of ∠ABC is 45º.