Question

1) OA= 10cm AB= 12cm OCLAB Find - CD=​

Answer 1

Given:

• Distance from point A to the origin O is 10cm.
• Distance from point B to point A is 12cm.
• Distance from origin O to point C is perpendicular to distance from point A to point B

To Find: Distance between point C and point D?

As the distance between origin O to point C and point A to point B is perpendicular then,

                                        AC = AB

(perpendicular from the centre to the chord always bisects the chord)

                             ∴         $AC = \frac{AB}{2}$

                                                = $\frac{12}{2}$ = $6cm$

In right Δ OCA,

                                            $OA^{2} = AC^{2} + OC^{2}$

                                            $(10^{2} ) = 6^{2} + OC^{2}$

                                          $(OC^{2} ) = 100 - 36$

                                             $OC^{2} = 64$

                                              $OC = \sqrt{64}$

                                              $OC = 8cm$

Now to find CD,

                                        $CD = OD - OC$

                                               = 10 - 8

                                               = 2cm

                           ∴      OA = OD = 10cm (radii}

Hence the distance from point C to Point D (CD) is 2cm.