Question

o is the centre of the circle the angle subtended by the arc BCD at the centre is 140 degree BC is produced by P find Angle B A D and angle DCP

Answer 1

Answer:

BAD=70°,BCD=110°

DCP=70°

Answer 2

Given:

• O is the centre of the circle.
• The angle subtended by the arc BCD at the centre is 140°.
• BC is produced to P.

To Find: Find the angle ∠BAD and ∠DCP?

explanation:

Since the arc BCD makes ∠$BOD$ at the centre,

                                        ∠BOD = 140°

∠$BAD$ at a point A on the circumference.

                             ∴          ∠$BAD$= $\frac{1}{2}$∠$BOD$

                                                     $= \frac{1}{2}$×(140°)

                                                     = 70°

Now,

     To Find the angle ∠DCP,

    In triangle ΔDBO,

                                       DO = BO

                                    ∠$BDO$ = ∠$DBO$

                                                = $180 - \frac{140}{2}$

                                                = 20°

                          ∴        ∠$DCP$ = ∠$DBP$ = 20°

                            ( angle on the same segment )

                                              ∠$DCP$ = 20°

                                     

Hence the angle BAD is 70° and angle DCP is 20°