Question

if TP and TQ are two tangents tp a circle with centre O so that <POQ =110 then <PTQ is equal to

Answer 1

Answer is 70* <POQ+<PTQ=180*
110*+<PTQ=180*
<PTQ=70*

Answer 2

HEYA, BUDDY !!

C O N C E P T :

In order to solve these types of questions, learn the basic properties of angles and also about the sum of interior angles of various shapes such as triangle, square, hexagon. Read the question carefully and extract all the data given in the question required to find the solution. Also remember, when you need to frame an equation and find the solution of the equations; to find the solutions the number of equations framed must be equal to the number of variables.

S O L U T I O N

Given:

• Tangents: TP and TQ

We know that, Radius is perpendicular to the tangent at the point of contact

Thus, OP ⊥ TP and OQ ⊥ TQ

→ Since the Tangents are Perpendicular to Radius

→ ∠OPT = 90º

→ ∠OQT = 90º

Now, POQT forms a Quadrilateral

We know that, Sum of all interior angles of a Quadrilateral = 360°

∠OPT + ∠POQ +∠OQT + ∠PTQ = 360°

→ 90° + 110º + 90° + PTQ = 360° (By Substituting)

→ ∠PTQ = 70°

Hence, alternative (B) is correct.