Question

Using ruler and compasses only.
a. Construct a triangle ABC with the following data
AB = 7 cm BC = 12 cm angle abc equal to 120 degree.
Draw a circle with BC as a diameter. Find a point p on circumference of a circle which is equidistant from AB AB and BC. Measure angle bcp

Answer 1

Given :  AB = 7 cm BC = 12 cm angle abc equal to 120 degree.

To find : Construct a triangle ABC,  Draw a circle with BC as a diameter.

Solution:

Step 1 : draw  a line segment AB = 7 cm

Step 2 :  Take appropriate compass width and taking B as center Draw a Semicircle intersecting  AB at  X

Step 3 : Keeping compass width Same taking X as center Draw an arc intersecting semicircle at Y

Step 4 : Keeping compass width Same taking Y as center Draw an arc intersecting semicircle at Z

Step 5 : Draw a Ray from B passing through Z

Step 6 : Taking Compass width = 12 cm & B as center intersect ray drawn in step 5 at   C

Step 7 : Join AC

Draw a circle with BC as a diameter.

Using Suitable compass width  More than half of the BC  

then Taking B  & C as centered draw arcs on both sides intersecting at M & N

Join M & N intersecting BC at O

Taking O as center taking Compass width = OB or OC , draw a circle

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