Question

If tangent PA and PB and a puint L to a cinta with centre o and inclined to each Other at angle 80 of so then ind LPOA​

Answer 1

Given:

• PA and PB are two tangents of a circle.

• ∠POA=80°

To Find:

• ∠POA=?

CONSTRUCTION: join OA, OB and OP

PROOF:

Since OA⊥PA and OB⊥PB

Then  ∠OAP=90° and ∠OAB=90°

In

ΔOAP & ΔOBP

OA=OB (radius)

OP=OP(common)

PA=PB ( lengths of tangent drawn from external )

∴ ΔOAP ≅ ΔOBP       (SSS congruency)

So,

[∠OPA=∠OPB            (by CPCT )]

So,

∠OPA=1/2∠APB

          =1/2×80°=40°

In ΔOPA,

∠POA+∠POB+∠OAP=180°

∠POA+40°+90°=180°

∠POA+130°=180°

∠POA=180°-130°

∠POA=50°

The value of ∠POA is 50°