Ex 14.5, 9 Draw any angle with vertex O. Take a point A on one of its arms and B on another such that OA = OB. Draw the perpendicular bisectors of (𝑂𝐴) ̅ and (𝑂𝐵) ̅. Let them meet at P. Is PA = PB
Let us consider an angle with vertex O
and points A & B such that
OA = OB
We need to draw perpendicular bisectors of OA and OB.
Drawing perpendicular bisector of OA
We follow these steps
1. With O as center, and radius more than half OA,
draw an arc on top and bottom of OA
With A as center and same radius as before,
draw an arc on top and bottom of OA
2. Where the two arcs intersect above OA is point X
and where the two arcs intersect below OA is point Y
Join XY
Thus, XY is the perpendicular bisector of OA
Now, we draw perpendicular bisector of OB
Drawing perpendicular bisector of OB
We follow these steps
1. With O as center, and radius more than half OB,
draw an arc on top and bottom of OB
With B as center and same radius as before,
draw an arc on top and bottom of OB
2. Where the two arcs intersect above OB is point M
and where the two arcs intersect below OB is point N
Join MN
Thus, MN is the perpendicular bisector of OB
Now,
Point where XY and MN meet is point P
We need to check if PA = PB
Joining PA and PB
Checking length of PA and PB by compass,
We note that their lengths are equal
∴ PA = PB

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.