Q23 of 47 Page 1

draw a circle of radius 4 cm. Draw two tangents to the circle inclined at an angle of 60° to each other.


STEPS OF CONSTRUCTION :


1. Draw a circle of radius 4 cm taking O as center.


2. Draw radii OA and OB such that ∠OAB = 120°


3. Draw perpendicular at points A and B and suppose the point they intersect is P.


4. PA and PB are required tangents with ∠APB = 60°


JUSTIFICATION :


In quadrilateral AOBP , By angle sum property of quadrilateral


∠OAP + ∠OBP + ∠APB + ∠AOB = 360°


90 + 90 + ∠APB + 120 = 360


∠APB = 60°


More from this chapter

All 47 →
21

Due to heavy floods in a State, thousands were rendered homeless. 50 schools collectively offered to the State Government to provide place and the canvas for 1, 500 tents to be fixed by the Government and decided to share the whole expenditure equality. The lower part of each tent is cylindrical of base radius 2.8 m and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs. 120 per sq. m, find the amount shared by each school to set up the tents.

What value is generated by the above problem? (Use π = 22/7)

 22

Prove that the lengths of the tangents drawn from an external point to a circle are equal.

 24

In fig. 7, two equal circles, with centers O and O’, touch each other at X. OO’ produced meets the circle with center O’ at A. AC is tangent to the circle with center O, at the point C. O’D is perpendicular to AC. Find the value of

25

Solve for x: