Question

In the above figure, PTU is the tangent at the point T to the circle QRST

and PQR is a straight line.

angle PQT =100 , angle UTS= 55 and PQ = QT.

find, giving your reasons in full, the size of

(a) angle TSR,

(b) angle TRQ,

(c) angle STR.

Answer 1

Step-by-step explanation:

please mark as brain list

Answer 2

Answer:

⇒i will explain properties of cyclic quadrilateral and that are my reasons regarding this.

Properties of Cyclic Quadrilateral

• The properties of a cyclic quadrilateral help us to identify this figure easily and to solve questions based on it. Some of the properties of a cyclic quadrilateral are given below:

• In a cyclic quadrilateral, all the four vertices of the quadrilateral lie on the circumference of the circle.

• The four sides of the inscribed quadrilateral are the four chords of the circle.

• The measure of an exterior angle at a vertex is equal to the opposite interior angle.

• In a cyclic quadrilateral, p × q = sum of product of opposite sides, where p and q are the diagonals.

• The perpendicular bisectors are always concurrent.

• The perpendicular bisectors of the four sides of the cyclic quadrilateral meet at the center O.

• The sum of a pair of opposite angles is 180° (supplementary). Let ∠A, ∠B, ∠C, and ∠D be the four angles of an inscribed quadrilateral. Then, ∠A+∠C=180° and ∠B+∠D=180°.

• By that here we know that TSR is 100 , because TRQ is 80.

∴  by using anglum of cyclic quadrate shown above we got,

                      STR=100.