Draw a pair of radii OAand OB such that angle BOA=120° . Draw lines perpendicular to OA and OB at A and B .these lines meet on the bisector of angle BOA at a point which external point and perpendicular lines are the required tangents . Construct and justify
Answers
Tangents drawn & OP is bisector of ∠BOA
Step-by-step explanation:
Step 1 : Draw a circle with center O using compass
Step 2 : Talke a point A on circle
Step 3 : Draw an angle of 120 deg at O on AO intersecting circle at B
Step 4 : Draw 90 deg angle at A on OA & B at OB and iintersect each other at P
PA & PB are tangents
Step 5 : Join OP
in Δ OAP & Δ OBP
OA = OB ( radius)
OP = OP ( common)
∠A = ∠B = 90°
=> Δ OAP ≅ ΔOBP
=> PA = PB ( equal Tangents)
& ∠AOP = ∠BOP
=> OP is bisector of ∠BOA
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