Question

draw a right triangle ABC where AB= 3cm,BC = 4cm,and <B= 90° . BD is a perpendicular From B on AC such that D lies on AC. A circle through B,C and D Is drawn . construt taNget from A to the circle
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Answer 1

Answer:

We follow the following steps.

Steps of construction

STEP I

Draw △ABC and perpendicular BD

from B on AC.

STEP II

Draw a circle with BC as a diameter. This circle will pass through D.

STEP III

Let O be the mid-point of BC. Join AO.

STEP IV

Draw a circle with AO as diameter. This

circle cuts the circle drawn in step II at B and P

STEP V

Join AP. AP and AB are desired

tangents drawn from A to the circle passing through B,C and D

Type II

CONSTRUCTION OF TANGENTS TO A CIRCLE FROM AN EXTERNAL POINT

WHEN CENTRE IS NOT KNOWN

Stepsofconstruction

STEP I

Let P be the external point from where the tangent is to be drawn to the given circle. Through P

draw a secant PAB to intersect the circle at A and

B (say).

STEP II

Produce AP to a point C such that AP=PC i.e, P is the mid-point of AC.

STEP III

Draw a semi-circle with BC as diameter.

STEP IV

Draw PD ⊥ CB, intersecting the semi-

the circle at D.

STEP V

with P as centre and PD as radius draw

arcs to intersect the given circle at T and T.

STEP VI

Join PT and PT. Then PT and PT are the required tangents.

STEPV

with P as centre and PD as radius draw

arcs to intersect the given circle at T and T.

STEP VI

Join PT and PT. Then PT and PT are the required tangents.

solution

Answer 2

draw a line BC =4 cm ...at B draw an angle of 90° using compass and then keeping the point of compass at B and opening the compass 3 cm , put an arc ..mark the point of intersection of arc and line as A ....you have got AB line ....now join A and C ...triangle ABC is a right triangle ...then open the compass , put the point of compass on B and make an arc on AC ...it will intersect AC at two points ,say K and L ...put the compass pin on K and mark an arc above AC and then put the compass pin on L and cut the arc made first by another arc ....Now join the point of intersection of these two arcs with point B ...the line joining the point of intersection and point B will intersect the AC at a point say D ..BD will be perpendicular from B on AC ....make the perpendicular bisector of BC ...say at point O the perpendicular bisector is intersecting BC ....put the tip of compass at O and then open it till B and make a circle ..it will pass through B,C and D......joint A and O...make perpendicular bisector of AO ...and then say you got point R through perpendicular bisector. now keeping the tip of compass at R you can open it till A and make a circle...then the circle which will be formed will intersect the first circle at two points say M and N ...join A and M and also join A and N....AM and AN are the required tangents.....