Bissoy.com
Doctors Medicines MCQs Q&A

AB and AC are the two tangents to a circle, whose radius is 6 cm. If ∠BAC = 60°, then what is the value (in cm) of √(AB2 + AC2)?

AB and AC are the two tangents to a circle, whose radius is 6 cm. If ∠BAC = 60°, then what is the value (in cm) of √(AB2 + AC2)? Correct Answer 6√6

[ alt="CGL T2 17 Feb 26-50 25Q Hindi hrev images Q3" src="//storage.googleapis.com/tb-img/production/18/12/CGL_T2_17_Feb_26-50_25Q_Hindi_hrev_images_Q3.PNG">

As given ∠BAC = 60° and we know that from an external point, all the tangents to the circle are of equal length so AB = AC.

∴ ∠BAO = ∠OAC = 60°/2 = 30°

Since ΔABO and ΔACO are right angle triangles;

∴ AB = AC = 6/tan30° = 6√3

∴ √(AB2 + AC2) = √(108 + 108) = 6√6 cm

Related Questions

Δ ABC এর ক্ষেত্রে-i. AB2=AC2+BC2+2BD.BCii. AB2=AC2+BC2-2BC.DCiii. ∠C=60° হলে, AB2=AC2+BC2-AC.BCনিচের কোনটি সঠিক?
Δ ABC এর ক্ষেত্রে- i. ∠C স্থূলকোণ হলে AB2 > AC2 + B2ii. ∠C সমকোণ হলে AB2 = AC2 + B2 iii. ∠C সূক্ষ্মকোণ হলে AC2 AB2 + BC2 নিচের কোনটি সঠিক?
For realizing a binary half-subtractor having two inputs A and B, the current set of logical expression for the outputs D (A minus B) and X (borrow) are 1. The difference output D = A̅B + AB̅ 2. The borrow output B = AB̅ Which of the above statements is/are correct? 
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’.
Which of the following statements is/are true? A: If two tangents, PA and PB, are formed on a circle from a point ‘P’ and OA and OB are the radius of the circle, then OAPB will be a cyclic quadrilateral. B: In a ΔABC, an incircle is formed with centre ‘O’. Then ∠BAC will be 180° less than the double of the angle made by side BC at the centre of the circle. C: The length of two tangents from a point, outside the circle, are always equal.
Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?
Given below are two quantities named I and II. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose among the possible answers. Quantity I: A circle whose radius is 56 cm and The Rectangle whose length and breadth are in the ratio 7 ∶ 22 respectively. The area of a circle is equal to the area of a rectangle then calculate the perimeter of the rectangle. Quantity II: A cylinder whose radius is (1/7) of the radius of the circle and the height of the cylinder is twice the radius of the circle and the area of the circle is 154 cm2 then, find the volume of the cylinder.
Choose the CORRECT option about the two tangents drawn to the circle from the external point? (1) The tangents subtend equal angles at the centre of the circle. (2) The tangents drawn from the external point to a circle are equal in length. (3) The tangents are equally inclined to the segment which joins the centre to that point.
Choose the CORRECT option about the two tangents drawn to the circle from the external point? (1) The tangents subtend equal angles at the centre of the circle. (2) The tangents drawn from the external point to a circle are equal in length. (3) The tangents are equally inclined to the segment which joins the centre to that point.