Q. 255.0( 2 Votes )

Draw a circle of radius 4 cm. Draw two tangents to the circle such that they include an angle of 135°.

Answer :

Consider a rough figure as shown DB and DC are tangents centre of circle is A



In quadrilateral ABDC


BDC = 135° …given


DBA = 90° …radius is perpendicular to tangent at point of contact


DCA = 90° …radius is perpendicular to tangent at point of contact


As the sum of angles of a quadrilateral is 360°


BDC + DBA + DCA + BAC = 360°


135° + 90° + 90° + BAC = 360°


315° + BAC = 360°


BAC = 45°


Now let us construct


Step1: Construct a circle of radius 4 cm mark the centre as A and draw radius AB



Step2: Using protractor draw the line at 45° to AB from point A and mark its intersection point with a circle as C join AC



Step3: Using protractor draw a line perpendicular to AB from point B because tangent is perpendicular to the radius. Thus this line is tangent to circle at point B



Step4: Using protractor draw a line perpendicular to AC from point C and mark the intersection point with a line drawn in step3 as D


Hence tangents DB and DC are ready at angle 135°



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