Saved Bookmarks
| 1. |
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 cm10√3 cm5√3 cm25 cm |
|
Answer» 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. |
|