Question

From an external point P, two tangents PA and PB are drawn to a circle with centre O.If ∠APB =40 find ∠OAB

Answer 1

Answer:

In A OAP & A OBP

A

OA = OB

(Both radius)

40°

PA = PB

(Lengths of tangent drawn from external point is equal)

OP = OP

(Common)

:: Δ ΟΑΡ = ΔΟΒΡ

(SSS congruency)

So, Z OPA = Z OPB

(CPCT)

So, Z OPA = < APB

== x 80° = 40°

In ΔΟΡΑ

Z POA+ZOPA + Z OAP = 180°

Z POA + 40° +90° = 180°

Z POA +130° = 180°

Z POA = 180° - 130⁰ = 50°

(Angle sum property of triangle)

So, A is the correct answer