#### Question

Circles with centres P and Q intersect at points A and B as shown in the figure. CBD is a segment and EBM is tangent to the circle with centre Q, at point B. If the circle are congruent; show that

CE = BD

#### Solution

Join AB and AD

EBM is a tangent and BD is a chord.

`∠`DBM = `∠`BAD (angles in alternate segments)

But, `∠`DBM = `∠` CBE (Vertically opposite angles)

∴ `∠`BAD = `∠`CBE

Since in the same circle or congruent circles, if angles are equal, then chords opposite to them are also equal.

Therefore, CE = BD

Is there an error in this question or solution?

Solution Circles with Centres P and Q Intersect at Points a and B as Shown in Figure. Cbd is a Segment and Ebm is Tangent to the Circle with Centre Q, at Point B. If the Circle Are Congruent; Show that Ce = Bd Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.