Question

Construct a triangle PQR, given RQ = 10 cm, ∠PRQ = 75o

and base RP = 8 cm.

Find by construction:

(i) The locus of points which are equidistant from QR and QP.

(ii) The locus of points which are equidistant from P and Q.

(iii) Mark the point O which satisfies conditions (i) and (ii).

Answer 1

Hope this is correct..

Answer 2

Constructed Triangle RQ = 10 cm , ∠PRQ = 75° and RP = 8 cm.

Step-by-step explanation:

Step  1: Draw a line segment RQ = 10 cm using ruler

Step 2 :  Draw an angle of 75° at R on RQ

Step 3 : Take a length of 8 cm from R on angle drawn in step 2 and label it is P

Step 4 : join PQ

Δ PQR is Constructed

(i) The locus of points which are equidistant from QR and QP.

Draw angle bisector of ∠PQR

Step 1 : Using compass taking some width taking Q as center , Cut QR & QP at A & B

Step 2 :  Taking some compass width taking A & B as center Draw intersecting arc at C

Step 3 : join QC & Extend  ,

Line will be  The locus of points which are equidistant from QR and QP

(ii) The locus of points which are equidistant from P and Q.

Draw perpendicular bisector of PQ

Step 1 : Using compass width slightly less than PQ taking P as center Draw arc on  both sides of PQ

Step 2 : Keeping same width of compass as in step 1 taking Q as center Draw arcs on  both sides of PQ such that it intersect arc drawn in step 2 at M & N

Step 3 : Join MN  & extend

Line is The locus of points which are equidistant from P and Q.

MN  intersecting Extended QC at O

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